>new variant to change the chess rules to accommodate a smaller board 5x6, 4x5 or 6x6 for even shorter games.

That makes no sense. You can have games as short as you want. Just play using a different time control. I play 1+2 (minute plus seconds) and those games last 2 to 3 minutes at most.

BTW with variants, you're not really playing chess anymore. You're playing a different game with chess pieces. Not all the strategy and tactics transfer well if at all.