If you go to Cat Fancy I am sure that they ahve some excellent articles on kitten proofing your home so Jax will not be stuck, but Kittens are Kittens and Jax will have to explore.
Thats great that he bonds with Your Dogs
And I have the feeling that Paizley will come around one day.
My Pouncer, also a Tortie hated Mr Scrappy but eventually came around and they were insperable after that.

Good Luck with the Socialization