There's a common phrase: "Vote with your feet." She's entrenched and defensive, to the point that she is vindictively killing PCs to punish players. That is never acceptable, and a very strong sign that this is beyond fixing without breaking it a bit more and starting over. You can talk to her outside the game, and that might help and is always worth trying first, but you've tried and at this point more words are unlikely to get through.
Your instinct to leave to avoid more strife, and continued unhappiness in a pastime that is supposed to be fulfilling, is right. You always have to be willing and ready to walk, else you're a willingly-captive audience. Words are hollow if you're going to stay no matter what she does. If you're going to stay, she doesn't need to change, right?
Leaving doesn't need to be hard for you or unpleasant for her
Be ready to walk, but don't try to use the idea of leaving to convince her to change, since threats aren't going to bring a defensive person out of their emotional bomb shelter. If there is no change, and it sounds like there won't be, walk.
When you leave the game, communicate clearly and without venom that this game isn't for you and that you won't be participating anymore. You don't need to justify or explain (which will just invite argument), just inform that you're not going to play. If she tries to argue with you, don't try to convince her (her permission isn't needed!), just respond by gently repeating that the game isn't for you and you won't be playing anymore, then remove yourself physically from the conversation.
You can use this calm repetition again later if she seeks you out to try to start an argument. Feel free to talk with her otherwise; she's your friend, after all. If she wants to talk about the game and you feel like it's an honest attempt to communicate, feel free to. If it becomes an argument, of it becomes an attempt to convince you to stay/return without actually changing anything, the best you can do is express your preference to not talk about that:
I prefer not to discuss returning to the game right now. How about we talk about something else?
You can repeat that as necessary when the conversation is going in unproductive directions. Also feel free to back it up with "You're my friend, but I don't want to have this conversation now" calm repetition+leaving response.
Leaving is the best thing that could happen to her as GM
She does need your help, and leaving is probably the biggest help you can give her. She can't continue like this if she ever wants to GM again. She needs to stop if she doesn't want to ruin friendships. You're doing her a favour by leaving, because leaving works.
Why does walking work? Actions speak louder than words and don't invite argument. She can't fight a person who isn't there and make them "stop being absent!" by flexing her GM muscles. You can't fight an absence, and absences don't provoke the fight/flight reflex that arguments do, but absence is very loud. And if she's not fighting, she has a chance of hearing the message sitting in that empty chair.
Walking also discharges any responsibility you might feel for the other players: you've broken the illusion that the gathering is socially OK, and shown them a way out. You've also shown the GM that the remaining players have a way out, and maybe they can now get through to her with words. But regardless, they're their own people and responsible for their own happiness and choices, so leaving also discharges your perceived responsibility: by trusting them to use their own words/actions to take care of their own needs.
I know you're not a native English speaker, but in many circles of general nerd culture in America and on the Internet, there is a phrase for what you're doing right now: your spaghetti is falling out of your pockets.
In all seriousness, though, you seem very anxious about your situation and you should take a step back and relax. You say you're good at improv, but it looks like you're already sweating bullets because your party got sidetracked instead of getting to the quest you wanted to take them on.
I'm going to put my direct answer to your question first and some general advice afterwards.
Your players probably won't miss their characters. Why? Well, you generated them, and even wrote up their backstories. These characters were never made by the players playing them, and while they might have grown attached over a few moments, I find it extremely unlikely that they'll shed tears over a party that lasted for four sessions... that they didn't even make themselves. Even if the characters are extremely cool and interesting, that element of personal attachment just isn't there, which allows the players to truly say that they helped create an exciting story with interesting characters. This obviously varies from person to person, but again, I find it very unlikely that your players would have grown very attached in this case.
Go out with a bang. You know that amazing epic encounter you were saving for the climax of the plot arc? Yeah, run it now. You'll have to make some tweaks because you obviously aren't quite there yet, but get them there as fast as possible. Feel free to kill off PCs or even have a TPK at this point; memorable deaths are often much better than "and then they lived happily ever after."
Here's a few things to keep in mind when starting your next campaign:
Your content will come to light eventually, and it will be good. The quests you've designed will always find a way to come forward. Even if your plot arc is entirely ruined by something the players did, you will be able to recycle the content you made but never ended up playing, and I encourage you to do so for your new campaign. The only things that are truly lost are "hard" materials, like NPC stat sheets, etc.
You're in control, and therefore, you set the tone. Sometimes, it is best to take a page out of Gygax's book; after all, this is your campaign, and you put a lot of effort into it. Obviously you shouldn't take the entire preface from the AD&D DM's Guide to heart, but there is a point where a DM should draw a line in order for there to be some kind of structure, assuming you want your campaign to go anywhere. If your players are goofing around and killing NPCs for no reason, or making light of important people in-character, then they should be ICly punished for it; reprimanded for insulting a nobleman, pursued for attacking innocents, etc. It is also very possible to play a serious game in character and laugh until you're blue in the face out of character. This frequently occurs in the Dark Heresy games that I've played and ran.
You had better get used to murdering your darlings. This is a phrase commonly used amongst writers and creative designers everywhere in the U.S. The phrase means that you'll have to scrap ideas frequently, including ones that you really, really liked, so you had better get used to it. The saying is intended for use in the writing, film, video game, and other industries where a publisher or producer oversees your work, constantly telling you what can and can't make it to the final product based on time and expenses. However, it works just as well for when your ideas can't make it to the game because your players did something insane. And, on a related note...
Plan less. I don't know how much effort you're putting into writing everything ahead of time now, but you might want to ease up on that. From what you're telling me about your role-playing experience, it seems like you've been playing in a "safe" and slow environment where you rarely, if ever, have to scrap or re-do material. This happens literally all the time in regular tabletop RPGs, thanks to the insanely unpredictable nature of 4-5 different people working together. It will save you a lot of anguish if you lay out a basic outline of what's going to happen and then add the details once you're sure the players will be arriving there next session, or maybe two sessions later.
It seems like you've learned a lot already OP, which is great, but scrapping a campaign after 4 sessions (and while your players are all enjoying it) is something you should really avoid. If everyone else is having fun, consider either shaking things up a bit and changing your own notes, or coming up with a way to set them back on track, which doesn't always need to feel contrived or railroad-y.
EDIT: Well, now that SevenSidedDie has made that edit to your post, there are a couple of details that I didn't quite catch before, no offense. Since you said you have a month between each session, it seems like you might be over-planning because you have a lot of time between sessions. Heck, you might even consider having more frequent sessions, if you can't stop yourself from overthinking it in the intervening months. If in-person is not an option, use Skype and/or Roll20.
Best Answer
You have two options. Talk to your DM, or Find a new DM.
End of the day, you can't force a person to change and No D&D is better than Bad D&D. So if your DM cannot be persuaded to change their DMing ways, your only other option is to find a new DM.
So, your only non-quitting/non-firing-the-DM approach is to get your DM, preferably alone, somewhere away from the game table and not during game-time—and have a chat. I strongly recommend trying to be non-confrontational—approach this as "we're trying to fix this" not "you are a bad person and you should feel bad." I say this even if you think your DM is being a bad person, simply because accusing someone of that immediately puts them on the defensive. Here are some recommended talking points:
D&D is supposed to be Fun. We are not having fun.
D&D is a social game in which everyone—the players and the DM—are supposed to have fun. The standing rule within D&D is simply that: Have Fun. If memory serves, the DMG even explicitly says that if a rule of the game is getting in the way of you guys having a good time—ignore it!
Express to your DM that you guys are not actually having fun. You put a lot of work into your characters and you want them to have fun adventures. And the fact that he kills your characters and then criticizes you for not being "good enough" makes you not want to keep playing in his games.
Keep in mind that some players like high difficulty games—games where the Players have to be very optimized and very skilled in order to survive and win. Acknowledge this. Then tell him that you (and your friends) aren't actually interested in that sort of game.
D&D is not (usually) adversarial
Maybe he doesn't understand the point of the DM. Maybe he doesn't understand that the DM is not supposed to be the enemy of the players—but the one who gives them challenges along the road of telling a story. It sounds like you've tried to communicate this—but it's a very important point.
The DM should only be seriously trying to kill the PCs if that's the sort of game the players want.
All else fails
Now, you bring the rest of the party in—make sure you're all on the same page, and talk to him about this as a group.
Inform him that as you guys are not having fun—you'd rather not play D&D with him as a DM. D&D is not about players being "Highly skilled, hyper-competent masters of the game," it's about friends getting together to have fun. As none of you are actually having fun with D&D as he is running it, there's not much point in continuing to play. So, if he's going to stick to his "Git Gud" guns as a DM (reminder: you're still trying to be non-inflammatory here--so don't use those words)—then you're all simply not interested in being players under him. He may be able to find some more hardcore players to DM for—but you're not really interested in playing a game the way he runs it.
Tell him that if he's willing to try running the sort of game you all want to play then you'd be happy to give it another go (if, in fact, you are). Otherwise—he's welcome to continue playing with the group as a player... but you'd rather not have him as DM.
I mean... end of the day, you guys showed up expecting to play Skyrim, and he's throwing Dark Souls at you. You're not playing the game you wanted to play.