How do the momentum and spin of negative energy electrons (particles in the Dirac sea) and positrons (holes in the Dirac sea) differ?

Electrons and positrons can each have any momentum or spin. It is when you demand that the total momentum and spin of a system of electrons and positrons is, for example, zero that there is a relation.

Forget the Dirac sea. As an explanation of positrons it is a flawed concept. As an explanation of positively charged holes in matter, it is a brilliant idea.