Far as I know - might be wrong though- ICAO and FAA are one and the same ?
Thats an incredibly arrogant thing to say...ICAO is a conglomerate of nations who choose to conform (partly or completely) to a set of aviation rules/regs. As an expat American living in Australia let me say that the US really doesn't conform very well to the ICAO standard. May have changed since I was there, but ICAO only gets a marginal mention in the Flight Information Handbook.
Back on topic though, you do seem to meet the requirements with your FAA CPL. Best of luck.