I had a cup of coffee with a friend of mine who owns a few GSX-R's.
1990 GSXR 1100, another one with a turbo and a genuine 1989 GSX-R 750R.
Reason you mentioned "K-model" is that's when (1989) Suzuki changed the engine from 1052cc to 1127cc.
Any 1127cc engine, or a Bandit 1200 engine is a good base for this kinda build, in Bandit engine you replace the clutch assembly with a GSX-R unit and you are good to go.
Juha
p.s. He also said some not so pretty things about the watercooled GSX-R's, but I'll just say they are not a good idea for this kind of project...