What if I wanted to run the 3ds demo of the game? How would I submit it?

I believe that would fall into the Handheld leaderboard. But not too sure what you mean by "demo"

The 3ds has a demo of the game. Though demos on the 3ds have a limited amount of plays so theoretically not a whole lot of runs could be done

Well I tried but was rejected

This game requires runs to be verified, and a moderator has rejected this run. Reason: A demo speedrun is not acceptable for full game boards.