What is the optimal way to remove salt from cooked meat?
Boiling in a large amount of water is probably the most efficient method. The water should be boiling to avoid spoilage and to promote fast diffusion, and there should be a lot of it to maximize the rate of diffusion. (Alternatively, you could replace the water one or more times during the process) Cutting up the pieces will speed up the process, but if time/texture/tastiness are not important then you can boil the stuff as long as you like.
As for the cooking process having affected how much salt can be drawn out: Possibly a bit. Chloride ions are known to bind to certain muscle proteins during the brining and cooking process. I would expect this to be a very minor effect, though. If you've ever tasted the meat left over from a long-cooking stock, you'll note how bland it can get.