I reckon you might just be ok if you get on it straight away.
You need to download some forms from the web. The first you need to send to the CAA (with some money!). The second, you need to send to the lovely FAA with copies of all your UK docs (and NO MONEY!
) specifiying the Flight Standards District Office (FSDO) in the US at which you would like to collect your licence.
The CAA will contact the FAA to verify that you are whom you claim to be and that you have the qualifications that you claim to have.
As soon as the FAA hear from the CAA, they will send you a verification letter which is valid (so far as I recall!) for six months. Once you have the letter- you then MAKE AN APPOINTMENT with the FSDO which you specified - then you present yourself there at the appointed time with all of your documents AND the FAA letter.
The FSDO will then issue you with a temporary "issued on the basis of" FAA PPL which is valid for 120 days. At some point thereafter (takes a couple of months) you will get a permanent FAA PPL sent to you. This is then vaid forever PROVIDED that the UK Licence on which it was based remains valid.
The FAA won't charge you a penny for any of this! If you've never flown in the USA before - you will quickly discover that America is the land of aviation opportunity. No landing fees, no approach fees, often no parking fees etc.
Their bread is horrible though and their beer sucks - so nowhere is perfect :-)
Have fun!
Julian