[johnnyrod]

I would go back and re-check your headstock bearings. If they're too tight they'll make it hard to avoid wobbles at low speed, because the subtlety will have gone from the movement. As long as you don't have any knock in the bearings, they're fine, they are not meant to provide any resistance to turning - quite the opposite!

You don't need the front wheel up to adjust them, just slacken the top bolt and adjust as you've described, checking the feel before you call it finished, then checking it again once it's all tightened up - sometimes tightening the locknut changes the bearing tension. It's a job you want to spend a bit of time on.

Regarding the flopping, is it on both lefts and rights? If it's mainly one side I'd check rear wheel alignment. Ride at 20-30mph, shut off throttle, hands off bars. See if it consistently wanders to one side (try it a few times).