I had a very similar reaction as I got started with GTD. Over time, your ideas certainly never stop completely, but as they're captured, you probably won't generate 350 new projects every two weeks.
I've had a solid GTD system in place for almost two years now, and I still have times when I'm scribbling on the backs of paper towels because I can't make it to my ubiquitous capture tool in the other room fast enough.
Merlin Mann of 43 Folders had a fantastic podcast about "The Beauty of 1.0" where he encouraged listeners to take those good ideas that they've had sitting on the backburner and at least start SOMETHING. I know it's sort of obvious, but this was a transformative moment for me.
I'd make sure you have a big stack of blank project lists and at least write out a Next Action (or future action) for as many ideas as you can. I doubt anyone has time for 353 projects a week, but you can always randomly pick, say, five of those sheets, and at least get them to 1.0.
I'm a big proponent of having lots of projects running at one time. So long as your deadlines for external projects are captured in your calendar, and you review frequently, there's no harm in having two pages of Next Actions for your own ideas. After all, if they're you're ideas, they're probably FUN projects that you're passionate about! I have five pages of Next Actions right now, but I'm never overwhelmed because all but ~25 are things I'm happy to do.
Many times an old idea I had is transformed a couple years later into a whole new idea, and I'm glad I can go back and look at my paper towel scribbles.