We had a similar discussion recently over in the Cyber Sleuth forum: https://www.speedrun.com/digimon_story_cyber_sleuth/thread/u5rhw
I think the points made there also apply in that case.
Hey Art, thanks for reaching out. I think it would probably be a misc category, but at the moment I'd refrain from making a leaderboard, unless there is more interest in Master Coloseum runs.
That being said, anyone interested is encouraged to also just post their runs of it here, so that we can track those runs and make the leaderboard then.
I've just transferred the rules over from the Cyber Sleuth for some consistency, dunno how they vanished here.
As for your questions: NG+ starts with the specific NG+ Option, by which you can transfer over anything from a formerly completed savefile. DLC is currently forbidden, but in NG+ it also wouldnt help you at all. Timing is done in real time, so either have a timer running or the length of the video.