My K1100LT (60,000 km) has a vibration at ~3000 rpm. Initially I retorqued the engine mounts to spec (~40 N-m) as directed by the Clymer manual. The 2 front rubber mounted ones were in fact quite loose, the rear 3 were tight. The vibration was a little bit reduced.
My bike shop found that the faring support bracket was sheared at the lower end and needed welding (probably caused by dirt road riding). A lot of the vibration stopped (but not all).
Another local BMW shop said that the main source of vibration in K1100's is a cracked header pipe where it joins to the muffler. Sure enough there is a crack in the header (I haven't fixed this yet - next week).
However I replaced the rubber mount between the muffler and the bracket attached to the centre stand mount (the original was actually bent). The vibes at ~3000 rpm immediately vanished.
I am hoping that the remaining lower level vibration will disappear after the header has been welded. I thought that this might be useful info on your web page since it is not that obvious to check the exhaust system as a source of vibration (not to me anyway).