Whoops, silly mistake there, thanks.
It doesn't matter which powerups you use, all scores are fair. I guess if you do get a time with mini mario though it'd be nice to say that you got it with him, or shell mario or whichever, just so we know. Since there's so many around the levels it might be a bit of a hassle to just stay small Mario all the time. Except for Giant Mario, he could probably exploit a big chunk of time somewhere by just ramming through stuff.
Just got 362 in 1-2.

Another second is possible as well! I can smell it. One time when i got 362 I messed up the end stairs clumsily, getting slightly stuck twice.
EDIT: God DAMN those red boxes are annoying!
YES! 373 on 1-4. That's all for now, i'm out of lives!