May be hard to find a nice bike in your target budget, although with the years you designate it may be possible. You might also want to consider a newer 1200 RTP. Those usually are a lot cheaper than civilian bikes, but clean ones are out there. Never owned an LT (although I did consider a K1300GT a while back), but I would recommend a 2010-2013 RT. Some high-mileage yet well cared for examples in your price range. Good luck with the search!