This answer includes a frame challenge.
0. Let go of the fallacy of perfect balance
What I am looking for is a good resolution, or compromise, so that my
players don't feel slighted and no one ends up with very high or very
low numbers, creating overshadowing or spotlighting issues.
Oddly enough, over the years that I played "roll 'em up" since 1975, we somehow managed to have fun without point buy. For decades. Loads of fun, with some characters a bit stronger than others. (Heck, even with point buy, please see "tiers" in 3.5 to see how "balance" can still be an issue).
Current experience: we rolled our characters in the 5e campaign I am in now. No point buy. I've known all of these guys since high school, except my nephew and the DM. That's since about mid 1970's. Differing personalities. Rolling is no obstacle to fun and success.
If all of you attend this game with "let's have fun" as the goal, then let's get to addressing your problem.
As stated, your problem isn't dice rolling or not, per the email extract you provided us. Your problem is the relationship between players and DM.
What problem should you solve first? "Player versus DM attitude."
Find Common Ground
Before session one, you need a face to face session with everybody who will play to iron out what you expect from the game, and what they expect. Listen, and then share what you expect and why you think point buy is a good idea. Then, as a full table of people, come to a consensus.
Rolling Doesn't Hurt
Rolling for stats is a 40 year old feature of RPG games that works well enough. If that is what all of your players want, where's the harm in letting them do that? Your forecasting drama and problems is not giving anyone, yourself included, the benefit of the doubt. You will all be able to have fun, regardless. Anyone griping later on gets "the look" and the following response: "you all agreed to roll for stats, let's press on with the game, make the best of the tools you have." Since you mentioned that this is the gaming group you've been with for 2.5 years, and you've been friends with some of them for about 15 years, you all already know how to have fun together. Have some faith in that already established track record.
If the opinion is divided among the players on this point, go back to point one and the pre-meeting to iron out expectations before character creation. Until you reach consensus, the game is at risk.
Play!
Once expectations are more or less aligned, play and have fun.
Have Fun!
If you aren't having fun, you are doing something wrong (as a group). That would be the topic of an entirely different question, after you all begin. I see this question as "an ounce of prevention" effort (a good idea as you know this group). Given that you've known each other a while, up to a long while, I'd be very surprised if you don't have fun if you start on the right foot. Consensus building is a means to that end that's pretty effective.
On a mechanical note, since this is 5e, an ASI (later) or a racial bonus (at start) can take the hard edge off of a low number.
Best Answer
I agree with the comment that using pre-generated characters is your best bet. I've used them successfully on one-shot campaigns, and players enjoy trying to find the character that they can most easily identify with. If you do go with pre-gens, it might be worth writing up a quick paragraph to describe the character's capabilities if you're playing with players who are not familiar with UPPs and what skills mean. In my game, I gave them the adventure backgrounder, let them choose characters and then had them shop for themselves. In my case though, I was able to email the characters, background and equipment list so the players were ready before hand. That may not work for you.
You can also have them roll UPP stats, then give them a set number of skill levels to buy skills with. You can decide if you want older, more experienced characters or relatively unskilled ones, then give them 2 skill points per 4 years of age (which I'll call "terms" to keep things simple), which is about how things average out. To keep things balanced, you could cap skill levels at the number of terms, but that may not be necessary.
Have each player choose a profession and then just buy skills off of the generation tables as they see fit, respecting the EDU limits for advanced education.
At the end of this process, give them a list of relevant skills for the adventure, and let them each choose one. This will make sure that they have certain critical skills that your adventure is assuming they will have.