If my memory serves... Mopars run the ring gear on the converter - not the flex plate, so starting it with the trans disconnected like you can with a Chev or some Fords is a no go. try 'stalling it up' to see if the vibe changes.
Someone other than me might suggest that you use a length of 3x1,1/2 pine to 'load up' the balancer, but in these days of litigation I could never suggest it. Pity you can't get into the bellhousing to lean on the converter....oops, same lawyer controlled deal. Good luck, like pepi said, check the ballancer.