The best way to handle attention-hogging "diva" players is to set limits, then enforce them.
Set Limits
Divas, whether in RPG groups or in real life, take advantage of the social expectation to be polite and accomodating in order to get away with their behavior. So to protect your own sanity and your game, you need to create an alternate social expectation up front. In the case of a play-by-post RPG, this could mean rules like "if you take longer than X days to post your actions, the GM will declare a neutral action for you and continue without you", and "if you're repeatedly unable to come up with actions or ideas for your character, the GM may ask you to create a new one you're more comfortable playing."
The key here is to set the limits as a group. Don't single out the diva (they'll probably feel singled out anyway, but that's beside the point), just take some time before or during the opening of the game to state these ground rules. Emphasize that they apply to everybody and that they will be enforced in order to keep the game running smoothly for all players.
Enforce Those Limits
An important part of setting limits is declaring how those limits will be enforced. Otherwise it's like a parent who says to their toddler, "You'd better get over here right now! I mean it! Now!" but never actually takes action to address non-compliance. The toddler knows she can ignore the warnings because nothing will happen to her if she does, and she gets to keep doing whatever she's doing anyway.
Therefore, once you've set your limits for the game, enforce them. If the diva player (or any other player) takes too long to post their actions, do as you said: declare a neutral action for them, then move on. Ignore whining and complaining; refer back to the limits established at the beginning of the game: "I understand you're frustrated. You agreed to the limit of X days at the beginning of the game, and it's been X days, so I had to move on for the sake of the rest of the players."
It's perfectly fair to give warnings (such as a message a day before the deadline saying "Hey, you agreed to post within X days and it's been X-1 days. Just wanted to give you a heads-up!"). However, the important part is enforcing the limit after it's been broken, and doing so consistently and calmly.
Keeping Your Own Sanity
Divas thrive on getting attention, whether positive or negative, from others. Setting and enforcing limits helps take away a lot of their avenues for getting this attention. They'll try to get it back by throwing tantrums, complaining, and otherwise table-flipping over the "unfair" rules and "getting picked on". This is why it's so important to set the limits for everyone at the beginning of the game. That way all you have to do is calmly and repeatedly fall back on, "You agreed to these rules. That's all there is to it." As long as you keep your calm and ignore the diva's attention grabs (and make sure the other players don't get drawn in), you'll remove the diva's incentive to act that way and make the game more enjoyable for everyone.
Note that this may result in the diva threatening to leave the group. If they do, say calmly, "it's your choice whether to leave or stay. If you stay, these are the rules you've agreed to." Then it's up to them whether to leave (and get no attention at all) or stay (and get less attention than they'd like, but still some). If they do actually leave, just say, "Thanks for gaming with us" and let them go. The point here is to not give them any attention, since that's what they're after. Giving them attention in response to threats or flouncing only reinforces that they can get what they want by doing these things. So just stay calm, be polite, and let the diva figure out that their bad behavior is no longer going to get them anywhere.
Your party is in the middle of a classic movie plot, where the team has an initial setback caused by a failure to work together effectively. Take heart that these stories have happy endings.
Real feelings come first
Your players seem to be really sniping at each other, and you want to make sure there are no ill feelings after people step away from the table.
Many experienced players can really get snide or even downright nasty in-character, and then stand up from the table and laugh about it. Other players, though, might get their “real” feelings hurt by comments about their character’s performance.
Please keep an eye out for this. If your players are getting truly upset with each other as people, not just as party members, you should take a little break from the game. Have a little fun with each other doing something else, until everyone cools off. (Maybe watch one of those movies with the teamwork theme.)
So they really like your knight...
A common trope in the “Learning to work together as a team” plot is the wise outsider who helps the team overcome its problems (The Sphinx in Mystery Men, the Vision in The Avengers, Gandalf in The Hobbit/LOTR, etc.) In your case, it’s the knight who came to their rescue. So yes, use the knight to help solve your party’s teamwork problem.
In and out of game issues
You now have 2 voices to deal with the bickering issues: your knight for game issues, and your own voice, for out-of-game issues. If things seem to be getting personal, use your own voice and step back from the game.
“Sir Coach-a-lot”
You want the party to be able to stand on their own, but right now they are teetering. Let the knight coach them along until their are ready to act alone.
Your knight might tell the party, “I am really getting too old to be an adventurer. But you are such a promising team. If you can rise above your current problems, I feel you are destined to do great things. Should you so see fit, I will try to help. May I accompany you for you next journey?”
This lets you model a humble spirit of teamwork, and sets the expectation that the knight’s help is for a limited time. The knight’s goal is not to become the leader of the party, but to make them capable of leading themselves.
Coaching, not Commanding
Feel free to give general tactical advice in the voice of the knight. The battle at the city wall might have gone differently if the party had hit the enemy a little harder early on; the knight can explain how important it is to gain the upper hand.
In battle, keep the knight’s advice as general as possible, ultimately devolving to simple encouragement, a la, “You know what do do!”
You might give your knight a heart-breaking backstory themed failing to save a companion, and how he has worked to redeem himself. The moral of the story being: Everyone makes mistakes, sometimes leading to calamity. But resiliency in the face of adversity is the true test.
Model Resiliency
Your knight’s prime purpose is to change the tenor of the party to one where the characters support each other instead of blaming each other when things go sideways. Let him be almost relentlessly supportive of the other characters, and relentlessly humble about his own accomplishments.
When a character snipes at another (“Aren’t you ever going to cast a spell?”) he might simply rephrase it in a more positive way (“Your magic will turn the tide!”)
If a character does make a serious mistake, the knight can model dealing with it in a mature and humble way. If one party member starts laying into another for a mistake, the knight can intervene, “If you are going to blame someone, blame me. I promised I would help you work as a team, and I have not yet succeeded.”
Saying Goodbye
Keep the arrow of this plot pointed squarely at, “the knight will leave the party as soon as possible.” He will do so when he deems the party is ready. This should provide the party a feeling of pride, being ready to face the world on their own.
The other way to remove the knight from the party is to see that he meets a tragic end, perhaps sacrificing himself to save the party. This has the advantage of forcing the party to really stand on its own, but be aware it would permanently take away a good tool you have to influence the party.
Do whichever you feel is appropriate for your story. Just don’t feel you need to kill him to get him out of the party. The last thing you want is for his death to be the trigger that starts your party bickering again.
Best Answer
Zachiel here, player in a living world (where problems of this sort keep showing up, I swear).
You say in a comment that the faster player's complaint is not that he's hot having anything else to do while the others are slowing down the game, but that they want to play their current character more.
We also know that it's forbidden to follow two missions at once, and that group rules dictate that party composition is out of your hands.
I see only one solution to this: be open with your players and tell them that the current group composition makes it impossible to provide a fun game for all of them. Ask them to party up with players with a similar schedule next time. If it is not possible or satisfying to abort this mission immediately and reallocate the players, keep your mission short.
Hopefully they will also see that your hands are tied. Depending on your players, telling them to take a look at the answers here might be a good idea.