Hell, I thought he was going to bed
Welcome from Spring Lake, Michigan !
If the rear tire is getting flat in the center, it can feel like what your describing.
I always had head shake if I let go of the bars with Mettzlers, after I switched to Avon Cobra it went away and never came back. Different issue, but Mettzlers are not the best tire for the bike.
Just curious as one can upset the drivability of the bike not installing them right and getting the motor cockeyed in the frame. Easy to check support motor from sump amd loosen the nut on the frint engine mount you should be able to spin the motormount bolt freely when the nuts loose.