All good suggestions. The problem with speed contests, even by puzzle size, is that anyone competing for speed would more than likely never choose any difficulty level other than "Easy". That wouldn't necessarily be very sporting. So then we'd have to break it down further into puzzle-size and difficulty, which would then set up 18 different speed contests per month. That isn't undoable, per se, but it certainly complicates things - especially when you consider 20 trophies awarded per contest, and that's 360 new trophies per month. It can really get out of hand.
I'm definitely not ruling it out though - I think it would be a lot of fun to have different competitive niches that people could choose to play for each month.