...cp_orange. Easy to tell if anyone's AFK in spawn, flank routes for me to take and avoid spawncamping, long range so my teammates and I can work on whatever sentries DO appear, potential for jumping on the enemy spawn, plentiful health packs in all the towers... it's the winner.

I mean, if you can find a no-cap KOTH you might have a massive advantage because of the lack of engineers but that all depends on if you still need to worry about a timer.

True, I didn't consider no sentries would also invalidate it. KOTH's the best gamemode for not dealing with engies, but it's also the shortest one, so that's out of the question. So... I guess a Trade or Achievement server? Probably one of those Trade_Minecraft_Realms servers where the only way out of spawn is into the battlefield.

Honestly I was going to state that teammates don't count anyways even if there was a way to do it. No-cap servers feel extremely gray to me since TF2 is an objective based game, but this is a combat based challenge where the goal isn't necessarily winning the match. I'll throw everyone a bone and say you don't have to see the match through to the end. As long as you get the stomp, you can win the match, lose the match, get kicked, leave, anything's fine as long as you get the stomp. This also means no-cap servers are on the table. For a challenge like this, I'd imagine the only maps worth considering are the ones where everyone agrees not to cap anyways. RTD and No Sentries absolutely invalidates the run though, one of them adds way too much chaos that could carry the run more than your own skill and disabling sentries directly changes the core gameplay.

Okay, so the most optimal loadout is the Force-A-Nature and Atomizer. They're the only Scout weapons with utility outside of damage (minus the Candy Cane, which makes grenades one-shot you), even if they fill the same niche. CTF is also entirely out of the question for turtling purposes. My best best is probably then Hightower. There are tons of pubs for it with capping disabled altogether. I have one favorited that's also usually populated AND that disables sentries, but it has RTD, which I assume qualifies as "changing the core gameplay".

I don't have anything else to ask about the challenge itself, but I did google "dominating a teammate" out of curiosity. Turns out, unless it was patched out, dominating an enemy the same frame you're autobalanced will carry over their domination, even when you're on the same team. So it's possible in *theory*.

The Winger as your only source of damage and form of killing period. If you can somehow build boost with only the winger, it's fair game. Similar story with melees, if you can reap the benefits without dealing damage it's fair game. Doesn't really matter if you've already dominated somebody, just act like you have no ammo in any shotgun and your baseball bat is made of cardboard (which is to say, don't use them in battle).
All I can really suggest for your strategy is find a match on Casual, Community Servers are only allowed if the plugins don't affect the core gameplay anyways so finding a good one is already a massive pain. I do think that's a pretty solid way to address the possibility of the enemy team dipping below 6. I'll update the rules to address some parts of your questions.

Also, what happens if the server drops below 6 players on a team after you start? I was originally going to suggest a two-minute grace period for people to rejoin, but then I realized I misread "12 players in the server" as "12 players on the team". Though that could be an extra-hard mode. Either way, it'd suck spending 30 minutes on one only for the player count to dip and having to restart. If it were up to me, every player you dominate who leaves would reduce the minimum server size by 1 (capping at 2 so it can't become dirt easy) so long as there's still an undominated player on the enemy team. Ideally you'll be writing down who you've already dominated in case they get revenge anyways, so this would give some wiggle room for people playing over longer sessions when players are more likely to log off without making the challenge itself easier. If the only people left are already dominated players and you STILL haven't reached the 6 minimum enemy doms, THEN it's a failure.

Actually, two more questions. One, is the challenge "dominate everyone on a server using only the Winger", or "dominate everyone on a server using ONLY the Winger"? For example, after I've already dominated someone, could I build Baby's Face Blaster boost off them? Push them off a cliff with the Shortstop and Force-A-Nature? Debuff them with the Fan-O-War? And generally clear them out with my primary once I KNOW they're in the clear?

**This is mainly because of turtling engineers, since Scout sucks at killing sentries and the most popular community servers are 2fort, Turbine and Hightower, ALL of which I end up dealing with turtlers on. If it's fair game after they're dominated, I can at least use the Shortstop to actually be capable of destroying a sentry. If it's not, I pretty much have to hunt down a server that doesn't lag my game from plugins (so I can actually aim) and that engie turtling isn't possible. Doesn't sound very likely.

(splitting them up cuz comment length)

I wish you good luck on your attempts, and I hope you can find a solution to the recording problem.

Changing the time would break my OBS recordings since their names are based on the time, but I admittedly didn't consider that. I still want to at least attempt it at some point, though.