I assume you know this already, but you can apply for a session even if you've already started a project. If you're nervous about starting a project because of needing money you should either do what agotterer suggested in fund raising, or just start your project on the side and keep day jobs until you can apply.

I can't speak for PG either but I would assume the chances that he'd fund you outside of a session aren't going to be any higher than during the lead up to a session, if anything the chances may go down.

Anyway, good luck!