I was just looking at those photos (really interesting to see, thanks for posting!) and don't see why the head stuffing couldn't just be removed - it looks like you cut a section away from the mouth gasket without any worries. As for the red mouth being glued to the gasket, well, the Kermit puppet's mouth plate is made of gasket, right? So you wouldn't have to detach the red from it?
It would still require major surgery - I can't imagine that that wire in the mouth would be easy to remove, and hollowing out Kermit's foam body and removing the wires from his arms and legs would be painful...but from what I can see a person with decent puppet-building skills would be able to turn this replica into a working puppet. Then again, a person with decent puppet-building skills should probably be able to build their own from scratch...