Type rides in sims in FAA land fall under part 142 of the regs. Part 142 schools have to follow an approved syllabus. You need to be able to present your ground and flight (sim) training records. It gets a bit cloudy if you have training overseas. The FAA says you can count foreign (to us) training for a FAA rating if it is given by an instructor rated in the country the training is given in. Face it, the 142 schools exist to make money and they are going to say "If you want to use our sim you have to go through our program."
That being said, you should not need a full program. Since you have time on the aircraft you should fall into something like an upgrade program. Maybe 32 classroom hours v. 80 for initial and 3 or 4 sims v. 6 or 7.
Airbus has a training center in Miami on 36th Street. And Higher Power in Fort Worth, Texas had a 320 training program a couple years ago, I think they still have it. I'd contact both of them, tell them your status and see what they can do for you.