OK, plane is balanced where it's supposed to be, but acts like it's not balanced where it's supposed to be...

Have you checked your incidences (i.e. the angle of the wing and tail plane)? The incidence angles and balance point work together and although people don't usually talk about incidence (because it's locked in), if youre wing is at the wrong angle the effect will be the same as if the CG is off. For a plane that acts unstable as though the CG were too far back, raise the leading edge a click at a time and you may see some big improvements.

I don't think this is a loose wing problem because your description sounds like it's happening during what should be straight flight, so no particular force change to make the wing pop up and cause this. I also don't think it will be fixed by reducing your throws (either mechanically or through exponential or low rate settings), again because it sounds like it's happening when you're not giving the plane input.

I'll be interested to hear more as you tweak the plane in... let us know what does the job once you get the problem fixed.