Ya, my 16 TB does it in 4th also. Spoked wheels and standard exhaust.
How many people with this issue are running Metzler tyres ?
Found a thread on a k1600 forum and they have the same problem at the same speeds and same gears. As that's an IL4 that eliminates the engine as a common cause. Anyway several of them found the fault was tyre specific. Metzler tyres made it worst setting up a 5hz osc at certain speeds, Michelin Pr3,4 it's there a little bit etc etc. I must admit I only noticed it for the first time touring in France/Spain and I fitted Metzler Roadtecs for the trip. Had the oem A3's before. Has got me wondering.