Ooh, good luck with your system!
I played in a fairly long-running game of Masks (a Powered by the Apocalypse game about teen superheroes), and it managed to not drag despite having a fair amount of action. Fights in that game weren't necessarily short, but I think they managed to stay engaging for a few reasons:
1. The situation materially changes with every post.
Basically, when a player deals damage to a villain, that villain marks a Condition - Angry, Afraid, Guilty, Hopeless, or Insecure. (The GM picks which Conditions the villain has ahead of time - more powerful villains get to pick more of them, and once they've marked all of their Conditions, they're out of the fight). Whenever a villain marks a Condition, they immediately take some kind of action related to it - an Angry villain might escalate things or blow something up, an Afraid villain might run away or try to take a hostage, or an Insecure villain might start to question their course of action or might double-down on it. In addition, a player who rolls well gets to pick some additional options alongside the damage - "take something from the opponent", "create an opportunity for someone else", "impress, surprise, or frighten the opponent" - and when a player misses, the GM gets to make something happen.
The upshot of all this is that you don't get stuck with two combat machines slowly whittling each other's HP away (or missing each other!) while you try to come up with interesting descriptions for "and then I stab him again". There's always something new to react to.
2. Fights have consequences beyond just expending resources.
Players in Masks have the same five Conditions that villains have, so by the end of a fight you're feeling Angry, and Guilty, and you need to do something about that if you want to stop suffering the penalties associated with those states. You generally clear conditions by having scenes where another character comforts or supports you (which involves a roll, and potential mechanical and story consequences), or by doing something specific to that condition (for Guilty, "fling yourself into easy relief". For Insecure, "take foolhardy action without consulting your team". For Angry, hurt someone important.).
Taking a bad hit can also have consequences in the moment - if a player rolls badly, they can pick from options like "dramatically lose control of your powers" or "cause collateral damage". I find that this helps each individual post matter more, and means the end of a long fight creates more story; it's rarely just "ok, after all that they're dead and we're down 50% on HP".
3. Combat isn't special.
Powered by the Apocalypse games don't break out initiative counts or anything like that when a fight starts. They stick to the way they usually work - the GM describes the situation, asks the players what they are doing, and occasionally someone describes something that triggers a roll. This holds in combat, which means that backing off and looking for better footing, taking cover and trying to talk to someone, etc. are all valid things to do, and not just a waste of a turn. During my game, in some fights we had multiple interesting posts go by without anyone actually making an attack. I find you also get a bit more dynamism - instead of "Ultron blasts you with his laser, you take 5 damage and now it's your turn", it's "Ultron takes aim, he's about to blast you, what do you do?" or "the Hulk grabs you, headbutts you, and tosses through the window while you're still reeling from his blow - and now you're plummeting towards the streets below, what do you do?"
Gushing about Masks aside, though, there's also some neat ideas in the way those games set up their moves that might be useful if you're looking at making things one roll. You often get lists of choices to pick from based on how well the roll went, like:
"If you roll 10+, choose 3 of the following options. On a 7-9, choose 2:
- You accomplish your objective.
- Your opponents don't accomplish their objective.
- Nobody you care about gets hurt.
- You don't make a new enemy."
Something along those lines could be a way to get more possible outcomes from the one roll, under the player's control - if they can't have everything, they can say something interesting about their priorities that potentially produces more story.
Aside from PbtA stuff, there's also some interesting conversation-based combat minigames in games like
Firebrands and
For the Honor. There's a minigame for representing a battle where each side keeps offering the other bait - "withdraw/submit now, or else your artillery fire takes out [one of my characters] and scatters the rest of my force" - until someone decides it's not worth risking further loses to keep the battle going, and another for 1-on-1 fights where the players take turns asking leading questions that describe the battle and give the other player a chance to reveal something about their character ("I overreach slightly and you have an opportunity to slip in a dirty little cut. Do you take it?"), until someone decides to ask a 'closing' question that can end it ("You get your sword’s point well between us, inside my guard. If you drive it home, you kill me. Do you drive it home, or do you allow me to step back and recover myself?"). I'm not sure how quickly those run, but I reckon there's some stuff there that could make for a good play-by-post!
Anyway, that's my wall of text. I get excited about systems. >.> Hope there's something useful to you in there!