You only need to do:
1. Commercial written test.
2. 3 hours of flying training in preparation for the checkride.
3. Checkride
Since you're already a JAA CPL you'd probably don't need TSA clearance, but you can check that at
www.flightschoolcandidates.gov
You don't need a visa since you're already a CPL.
You can do it in the UK or in the US.
PM me if you have further questions.
CFI