Curious that wobble started suddenly. You would think that normal wear mechanisms would not trigger a sudden wobble. Even though you say there is no play maybe a head bearing suddenly seated a fraction. And besides absence of play there should be some preload to provide a damping effect. Definitely check the rear end as well as the front. Could a damper have suddenly failed.
interestingly in the /7 and earlier the prime cause for the sudden head shake was the absurd top plate used instead of a proper fork top bridge. The failure mode of the plate usually started after the thing had been disturbed for some reason (like changing bearings). If the aluminium crown nut was not tight enough the secondary effect was fretting against the plate, counter intuitively the effect of soft metal fretting against harder metal usually means that the hard metal comes off second best. Before long the fretting sufficiently alters the shape of both the plate and the nut so that the only cure to the wobbles is replacement of both.
Now, the R65 top bridge is a far, far better thing, but I suspect that if not correctly tightened could lead to a similar fault developing.
My advice to the OP is this.
Start at the rear, check wheel bearings and then swingarm bearings. If they check out check front wheel bearings.
Next check the front forks for alignment and for STATIC movement in the head-stem bearings, check the preload whilst you are there.
Then put two of your biggest and heaviest friends on the bike and have them hold the front brake hard on (or put the bike against a stout wall) and lunge the bike forward - you at this point will have the dashboard off and will have your fingers under the top bridge and against the headstem.
If you feel or see any movement in the top bridge, you have found your fault. If you cannot immediately buy a serviceable top bridge, you can have a machine shop insert a sleeve.
And then do not ever leave the top bridge crown nut loose again.
PS, I have never had a case of the wobble in an R65 that wasn't a rear end problem, but i do remember being nearly flicked off my R100 several times before I twigged what the problem was. Which is why to this day my R100 wears a luftmeister top bridge.