The 2009 ZX6R is a 599, not a 636, but it uses a 51mm fork tube instead of a 50mm tube like other ZX6R's, so you would need to use 2009-2012 ZX6R triples or machine other triples to fit. I'm sure with enough work they will fit, but it would be way easier to use some previously scienced out older ZX6R triples and forks or some ZX10R forks.
My motor is all internally stock. The clutch springs have been shimmed and I changed the plugs, but other than that all the internals are stock. I have thought about doing some work on the head, such as a mild port on the exhaust side, an intake cam on the exhaust side, and little bit milled off to bump the compression up. All those things should be worth about 8-10 hp, but for now I am happy with something reliable and the ability to run 87 octane.