First, you don't need to say "If I were to be he/him". Just say "If I were he/him".
The answer is that both are correct, though nominative "he" is very formal, while accusative "him" is considerably more common and natural.
Incidentally, your example is not subjunctive. This use of "were" is called the Irrealis mood. There is no past subjunctive in English, despite what the books may say!