Unfortunately no, screenshots do not count as sufficient proof. The reason for this is that cheating through save-manipulation is extremely easy in this game, so we need every bit of evidence for a run's legitimacy that we can get.
Yes, you can turn off the music in the game settings and still get your run verified. It says so in the "Game Rules" as well.
Hi HopeXenoblade
While I absolutely understand your point, I feel like we already have a lot of redundant categories for this game that might never see any play.
You can try talking to other people in the community about this, and if enough of you guys want to split the categories then we'll do it. You could eventually try to do so on the Discord server. As it stands now though, it seems unlikely to happen.
A wonderful day to you too!
Scientia