You don't need a category to be added to the site to run it, to be clear. If you have an idea for something you want to run that doesn't exist already, you're always free to give it a shot and make a ruleset that you want to play.
A game doesn't need a board on the site. Feel free to run it if you've like and if someone else comes along that would like a leaderboard to exist and is fine with that responsibility they'll request it.
Any roguelike or game with randomized generation would fit your definition.
Sorry for the delay, this is already a Misc category in the SUPERHOT board.
It's a very niche community within a niche community. I wouldn't say it particularly helps any games at all "exposure-wise" to have people pump out a run for it that also run a few hundred games but it's also not hurting anyone. I personally don't request games on here unless I've gotten to a point where I'm taking the game more seriously, just to respect the time of the folks that have to approve games, but some folks feel differently.
It's definitely not for me but unless people are spamming game requests and abandoning boards it's kinda whatever.
Would not continuously rely on the same form of contacting someone especially after not receiving a reply that way.
From the inactive moderator request page:
"Moderators are considered inactive if they have not logged on or verified a pending run in at least 21 days. In the case of inactive game moderators, please attempt to contact them via social media to resolve the situation. If a Super Moderator is inactive, we require other moderators to perform a substantial amount of effort themselves in reaching out to these inactive Super Moderators in order to request that they remove themselves first.
If a game's moderators are highly inactive (have not logged on in three or more months) and not responding to off-site contact, and you have a run already on the boards, you may request moderation of the game without a pending run. Accepting these requests are at the discretion of site staff. In terms of requesting the removal of inactive Super Moderators, the removal of inactive Super Moderators should be requested by other moderators of the same leaderboard."
https://www.speedrun.com/knowledgebase/supporthub/request-moderation
Go to the Cuphead forums and ask there. This is a general forum.
To chime in very late about the last part- Superhot, being a game where time only moves when you do, has two modes for individual level runs in terms of it timing is based off real time or "game time" as if you had played at full speed. Both are their own category.
Think you'd just have to determine if the slow feature is integral enough to your game where it's worth having two timer modes, or if not I would default to 'real time' and keep it going full speed during the slow.
Other people have already mentioned the usual advice so I won't pile on, but best of luck!
You can run it if you'd like regardless of it being a category on here
If you can stream to twitch, turn on the option to save past broadcasts, then highlight your times after the stream.