Harpoon wars, headshot wars, one in the chamber, and team deathmatch would be a bit more interesting if they were time limit based and respawning adding, I would not remove the current ones, just make this as 3 new rounds. The fact is so many times on those rounds you end up dying by some stupid spawn or lag or other dumb things, and your skill can't be showcased. Not to mention by adding a time limit, you would have a shorter round as well, as many fun rounds people are sooo scared about dying that they just camp. The only change needed past that would also be to limit the points per kill.
Hey, I just don't see this as something that could really benefit the fun round pool. Things you need to consider are: The spawns on most TTT maps are very close together; just as with gun-game, spawn killing would still be a huge issue where players could camp a spawn. Players could still camp during these timed rounds. Staff members slay other people for hiding during fun rounds. The environment wouldn't be as lax since there would be a time limit. Could you potentially add a points distribution concept, spawn killing mitigation tool, and a time limit you would want us to consider to your suggestion?
The point would be to get the most kills, spawn killing would still be a thing but its already dealth with on gungame rounds on map like innomotel or pool. Players can camp all they want but chances are they wont get as many kills as they could by running around. Staff members wouldn't have to slay as the round would be timed and set to a duration shorter than most other fun rounds, so it wouldn't be disruptive to gameplay. The environment would be more lax, during headshot wars or harpoon wars I'm always concerned I'll get shot from the side or some angle that I can't cover but if its a time limit you simply respawn and try again As for points, make it like 5 points per kill or less, add point score for most points and thats it, for spawn killing if you were crazy enough you could blacklist maps where everyone spawns together.