balanced flex plate on balanced 360 cid

I agree. More than likely, if it is a balanced race engine, and it had the Fluid dampner on it when you got it , it is internal balance. I would again, ask the guy you bought it from what flex plate/convertor combo he was running. Hopefully, you can get a way with just running a nuetral balanced flex plate.

I built a hot little 340 one time and used my existing 318 flywheel, so I know the vibes you are feeling. As soon as I got the correct flywheel on there, it was as smooth as glass and rev'd to the moon. Until you get it figured out, I wouldn't drive or rev it any more than absolutely necessary.

Let us know how this turns out.