These bikes have a tendency to stick the piston rings when not driven or only driven old man style, run really warm (15-20 miles) and do some high revs runs to free up the rings, it might take several runs!!
Indeed 560 bucks well spend. Just get new tires and take it for a couple of long rides. It will run much better after that. The fuel lines and the fuel pump mount are not ethanol resistent. Replacing that will save you a fuel pump breakdown in the future. I had a K100 RT with about the same miles on the clock, had a lots of fun with it. Well maintained and used every now and than, they will last forever.
Nice vid, I have four of them in my garage. These engines are almost unbreakeable….just put new tires on it, bleed the brakes and go for a long ride. Cleck valveclearance!…..I pulled a few out of hibernation and riding them makes them almost like new. Sidenote, the engines have very hard cilinderwalls, worn rings are not the issue, just that oil (I put 20w50 mineral in all four) is leaking when on the sidestand. But this you know now. You will Enjoy this bike!