> odds are heavily against this idea actually being novel or non-trivial to someone with more formal training

That last line puts you way ahead of most amateur researchers.  In my personal experience most of them [follow this line of thought.][1]  If you're interested in talking about your idea with researchers, look up a prof in the field at a local college and write something like

> I'm John, a software engineer with an interest in research in your field.  I've come up with an idea I think is interesting and would like to know more about it.  I was wondering if you or a knowledgeable student might be interested in helping me understand it better.  I know you and your students time is valuable, and I can offer some money if someone would be willing to help me understand this better.  (Be sure to attached an explanation of your idea)

I've never had someone offer me money out of the blue, but if I did, I would likely find a student who would really appreciate an extra $50-$100 for explaining it.  There may also be scholarly meet-ups a grad-student could direct you to.

Although it sounds like your expectations are not sky high, don't expect to have discovered anything revolutionary, and please be nice to whomever ends up helping you, and don't try to convince them you are an unrecognized genius toiling away in your basement. 

  [1]: http://academia.stackexchange.com/questions/20674/handling-unsolicited-proofs-of-famous-mathematical-problems?lq=1