Another possibilty is a thrust line or vertical stab out of alignment. Many of my planes will "tuck" in a tight turn, rolling one way in to an inverted situation like you describe, when something is out of alignment. The problem often doesn't show up at normal speeds.

If you turn hard to the right, does the plane kind of spiral up and try to start rolling out of the turn if you hold it long enough? It's usually not nearly as violent as the "downwards" tuck, but if you get that same effect, it's worth looking at.

Do check the pushrods and such as Joe said though, that's the first place to look.