competitions for grants
Oh, grants. That's an entirely different kind of thing. You need to research grants, not GDD contests.
1. Maybe I could submit my GDD to a studio.
2. Would any of you know where to start on that? I know what publishers might take a look, but I'm not sure how to begin and get their attention.
1. Maybe you could, but studios (developers) don't have money. Publishers do.
2. Read FAQs 11, 21, and 35 at http://sloperama.com/advice.html