My K1100RS handled similarly until such time as I changed out the rear tyre. It had worn flat, but not terribly obviously. I think the pressure you're using at the front is too high, but I don't think it would have that effect. Perhaps your tyres are old and hard, no matter how little use they've had? Not impossible on an older bike with periods out of use. Are your wheel bolts done up properly? Also, remove the rear wheel and check for movement in the final drive joint, there are some pins (the name escapes me) that wear. Look for side to side movement. All that said, sure sounds like steering head bearings though, as mentioned earlier.
Martin the other
in the sunny Riverina