It sounds like you've got something loose, (start with the main gear and work your way up), or out of balance.

Have you balanced the main blades? Have you checked the blade tracking?

I'd think the tail rotor being out of balance would give the tail a bounce - which wouldn't fit what you describe.

And the tail fin won't cause the problem either. I've got to wonder about the "twisting", though. The tail fin was twisting? Along the tail boom's axis? Sounds like it needs to be checked and tightened.

I'll have to defer on the gyro question, but it sounds like a part I'd be replacing. Since it works for a while, then stops, it sounds to me like it's goin' bad.

Good luck.