I have just done all this without leaving UK and I am waiting to do my BFR.
It is possible to get the 'piggy back' FAA PPL without leaving the UK, issued on the basis of the validity and ratings of you JAA PPL.
I must say that with the help of PPrune etc I have found the whole process straightforward and I now have the FAA temp airman certficate and am looking for a convenient time to do the flight review.
It does seem to make sense to do this in the UK as the meeting to validate your licence takes 15 minutes and unless you were planning to do some flying straight after BFR in US it seems reasonable to save yourself the trip.
Once you have been through the steps outlined above the key is to make an appt to see Adam House. He is the FAA man in the UK and can do what you would otherwise do in New York. In fact it was the New York FSDO that suggested I see him rather than travel to US when I was making my appointment with them on the phone.
Steps to complete
Form to CAA to validate your JAA PPL for FAA
Check that FAA have received your form - you will get a letter from them you need to keep original
Check that your nominated FSDO has received letter (New York if you dont want to leave UK)
Check that they have it on file in New York office (a few phone calls)
Make appt to see Adam House (you need to be time and geographically flexible in UK)
Complete paper work AH (he will send a check list to you) and pay fee.
Leave with temp airman certificate.
Arrange BFR and validate your FAA PPL
All achievable without leaving UK.