Some ideas
I was a cfi in Florida a few years back and we just went straight to the faa office and got the faa certificate (based on your certicicate) right off. This was for vfr ppl only. We generally discouraged ifr flight for the new, overseas pilots. We tried to fix them up with a saftey pilot that was a local hour builder too if they wanted ifr... just our experience with language problems, local geography etc.
If you go to florida, the FAA is in Tampa, Orlando, Jacksonville, Miami and others.
I did all this pre-911 so some of the rules I expect are a little strickter now.
I might be talking with my FAA guy in the next few days and will ask him. Also, ASK the FBO/School you plan to go to. I am sure they will take care of you and tell you any of thier own rental rules. (The school I worked at is gone now ... 911)
I have not been to any of these schools in years but you can check into
Clearwater FLorida, We have Clearwater executive (phone 727 461 5229)
St Petersburg international has several schools, here are two 727 538 2088, 727 531 3545.
St Petersburg/Albert Whitted. Bayair 727 822 4216 (Ask for Misa..good friend)
About 80 km north (a bit in the country for non-flying activities) Crystal River airport. They also have gliders.
In the tampa area ... Vandenburg airport, Peter O'Knight airport, Zepherhills.
I am trying to give you local places that are not the BIG schools. If you have questions ... let me know as I live here. Again, I have not done any GA stuf in years (airline now) and the rules are a little different now.
We don\'t require a rt certicicate for domestic flying here.