I don't want to cheat. But I do think I'd like to release a jam build and then maybe a few days or a week later release a more finished polished version in case anyone ends up wanting it.

Would I just create a second project for that? To avoid confusing anyone about the update not being qualified? Or after X days will it no longer matter and I can post updates to the main project page?

The jam is set to so you will be restricted from uploading new versions during the voting period.

I THINK (not 100% sure but I've seen other people do it) that you'd be able to upload an alternative set of files during that time. 

Either way after voting is complete it's just like a normal game page and you can make as many changes to it as you like