Hi John,
I had the K1100 LT SE, found it to be a lovely bike and very comfortable, the best screen I've ever ridden with, providing the electrical side works that is. I think the ABS can be a weakness but can also be disconnected as a cheaper option than repair or replacement.
The riding position was spot on and handlebar seat relationship near perfect for me, the only downside I found was that on a motorway the bike could have done with an extra gear or higher gear ratios as can be a little buzzy at speed. The exhaust are known to crack at the headers making it an expensive replacement if not repairable.
I now run a ST1100 Pan European and find the engine to be far smoother and tractable with more power and relaxing on a long run, the original screen on the pan was useless but having fitted an MRA Vario it's almost as good as the Beemer screen.
I hope this helps and good luck with the purchase if you go for it, lovely bikes and good value for money if the price is reasonable.