My opinion: If your H1B is under processing (you expect result by the end of Sept) and if approved, there is no need for TPS. So, wait until Sept and if you did not get H1B, then you still have time for filing TPS with EAD.

Next, what happens if you file TPS now when your H1B is not decided ? If you receive TPS before H1B (which is not the case as TPS takes some time and goes beyond Sept by the time you receive EAD), then your H1B will be void.

I might be wrong but that's what I lawyer says.