Would it be any sort of violation of the letter or the spirit of the Jam if the base rules were all on one page, and maybe advanced supplemental options were available? Or does that look too much like a workaround for an overlong project?

I'm thinking like a 3-class Fighter/Mage/Rogue base, and a half-page Paladin/Assassin expansion for advanced play or something in that vein. A later development to turn a solo/small combat game into military siege engine combat scenarios, maybe.

You're allowed to use both sides of the page, so that should be okay. However, if you're going to a new page entirely I think that would be against the rules, yes. 

Good game idea, though. 

I've updated the FAQ to better address 'extra' material. Hopefully the below section helps answer your question.

Can I include extra pages for character sheets or extra character options, adventures, bestiaries, tokens, etc.?

As long as the core rules fit onto a single sheet, and a player/group could pick up that page and happily run that game without the extra pages, then you're good to go. 

You could include optional rules on an extra page specific to using that extra content (e.g random encounter rules on a hex map adventure) however anything that is required to play the game should be available to the players on the main page.

The important thing is that your submission is not multiple pages of text that players (including a GM if the game requires one) have to read first in order to play your game.