Wayne,
That's the exact scenario that AGR413 described with the CG at 10.5" He said after he moved it to 10.25" the problem went away. I have to agree with you that the flat bottom stab is probably the culprit. Does seem odd that it would nose dive if it's tail heavy but this seems to be the case. Let us know what the outcome is if you decide to move the CG back even further.