RE: GSP's and cats?
If you start with a kitten it might work.
It is pretty basic - if the cat runs, it kicks in the chase instinct. If You start with a kitten and don't give it a place to run (and providing your dog doesn't eat it the first day) they may make friends, or at least tolerate one another.
My hunting dogs just ignore the farm cats at the farm (but then these cats don't run from them).