All comments are certainly appreciated!
When we were getting started, my cofounder and I held off on putting a single word to paper until we were out of our full-time jobs, on the advice of our lawyers.
I'd just go and talk with your employers about it. "Hey, I'm really happy here, but I've been thinking about a side project - I wanted to arrange with HR that it was my own invention and belonged to me, of course it won't interfere with my job which is my first priority..." Employers want to keep good people so if your side project is truly unrelated to your current company it hopefully won't be a problem.
I'm not sure how litigious they are, and in the end I don't think they'd care about me and my idea. It wouldn't compete directly at all. I guess I'm more concerned about what a VC or Angel investor would think or if that would hold up the process or scare of other potential investors. Or if I beat the odds and did end up selling it one day, I'm worried that any company like mine might see an opportunity to snaggle things up in order to cash in on the winnings. Its a good company, and I enjoy it here, but I just want to keep things clean.