G, you already hold an ICAO ATP(H)
Your skills will not markedly improve by douing an FAA ATP (H) check ride,
The ATP (fixed wing or rotorcraft) is experience based and no sign off is required from a CFI for the initial check ride.
You don't need TSA threat asessment either for the same reason.
You are moving sideways if you will from JAA ATP to FAA ATP, you do not become more or less of a threat.