I would like to add that it's happened before, perhaps more often than you think.
The most immediate example that comes to my mind is the
QSST by SAI LLC which was designed upon their behalf by Lockheed. On the other hand, I imagine this required, at the very least, a hefty sum of venture capital and other financial favors/conditions imposed by Lockheed (especially given the relatively high risk of this venture).
I cannot tell you what the best idea is aside from what already has been advocated, other than to either contact the companies directly (Airbus actually has a policy for free submissions and a form on their website; NG has a policy strictly forbidding free submissions and Boeing is somewhere in between; trust me you're not the only one who thought/thinks he has a brilliant aerospace idea

), contact someone with connections or experience (boards like this are at least a start) or, depending on how "married" to your idea you are, just keep talking/publicizing it and hope someone will like it (though many companies are hesitant to pick up "free ideas" because of copyright issues).
Also - depending on what exactly your idea is - you could, at least theoretically, build an R/C subscale demonstrator yourself. That's what
FanWing LTD did, using nothing but common R/C components.