STARCONTROLUNKNOWN'S: BATTLEGROUNDS - or colloquially, STUNKBAT... or I guess STUBG?
I don't know about this arena-thing. I guess the biggest thing for me is the suspension of disbelief necessary to legitimize the arena in space. We're in a perfectly circular, single-plane ring/arena, made out of asteroids? How did we end up inside this ring? How do you get out once you win? Why does it contract (like the aforementioned PUBG)? Since we're just showing one plane, can't you just like... step to the left a little, and miss them entirely? Or make a hard left into the depths and fly away from the plane the asteroids are on?
I'm not in favor of a 3d battlefield, but I feel like an arena like this calls attention to the shortcomings of a 2D plane playing area. And on top of that, it feels very game-y.
Also, I feel like we're coming up with this entire system to avoid the problem of "some battles may go on too long because of kiting".... but jeezes, what is that? 1% of games? So much so, that we have to change the game with slapping a time limit on each round and a contracting belt of asteroids that forces engagement for no apparent reason. It's just weird.
And again, it just makes the whole thing feel like a "game", which is a dirty word. Maybe I'm not the target audience, I guess. Maybe people love set arenas, and time limits, and forced engagement to move up the rankings and yadda yadda. I'll never be into that, I'd just blast some ships and if I lost them, no big deal. The thing I liked about the wrap was that it felt like even though it was a 2D plane, you had this perception that space was spherical and despite flying "away" from a planet, you were really just flying around the planet and would end up in front of it again, since it was an unlimited playing space based on the curvature of space, rather than linearity.
Actually, that gives me an idea....... I think it would be possible to implement some form of this:
Keep the 2D plane. But make it a sphere... like, a bubble? What if we put in a system that, when you got to the edge of this invisible "sphere", there was an animation of your ship PIVOTING - going into the depth for a second and transitioning to a NEW plane, the ship actually curving off into the distance for a second, the camera swoops down to eye-level cinematically, following the curve, before leveling out again and facing right back at the opponent? Meanwhile, the opponent has closed some distance, and the planet view rotates to keep consistency. Does that make sense to anyone? I can see it in my head. Here's a very rudimentary drawing of the temporary camera-shift:

Anyway, that's my proposed solution. It's just a tiny little slap on the hand for trying to constantly flee, rather than impose all these forced, inexplicable constraints on things.
As for the player-made questing? Shit, count me IN. But you just left us with that tasty morsel, and no explanation on how to submit? This is the best thing ever. How do I sign up and send my ideas?! I've got a few that I know would work well in this universe. MOAR! Tell us MOAR!