Is it theoretically possible to have a stable, non-radioactive transuranic element?

If our understanding of the electric force and the strong and weak nuclear interactions is correct, then no, it is not possible. The nuclear interactions operate over extremely short distances. The electric force obeys linear superposition. Basically, that means the electric fields due to all the particles simply add. In a large nucleus, there's no way for the nuclear interactions to be strong enough to overcome the electrostatic repulsion of the protons.