Conversion? Not really for a stand alone
As some who has done this in the past (almost 20 years ago!), I can tell you that it is(or at least it was!) far easier than FAA to JAA/CAA and a lot cheaper.
You will have to work closely with your training organisation, their examiner and the local FAA FSDO (Flight Standards District Office - one in each major city/region).
Essentially, to get a stand-alone FAA ATP (they don't call it an ATPL because it's actually a Certificate, size of a credit card with all the relevant stuff on both sides), you will need to do the following:
1. Start studying for the ATP writtens and do the exam - no big deal if you are already a commercial pilot and have a foreign ATPL.
2. You will have to do an ATP check-ride. Either in an aircraft (but only if you go for a generic MEL rating, ie. No type rating). In your caseyou will be doing it in the sim. There are plenty of places that do a combined FAA ATP with a type - usually a B737 is the most common.
3. You must choose your training place carefully and make sure you tell the folks who are doing the training and checking EXACTLY what you want. From what I understand, you are seeking a FAA ATP certificate with an A320 or some other type.
4. You will need to do a full Class 1 FAA medical with a FAA AME. I would do this BEFORE you start training to save you time. Not that expensive and if you already have a JAA medical, no prblem. Somtimes you can find AMEs who do both! This will save you money and you can get two for the price of one - JAA and FAA.
So, a little bit of paperwork, effort and money but a far EASIER proposition than getting a JAA ATPL from scratch. You should be able to do all this well inside a month depending how much studying you've done.
Hope this helps and hood luck! Now if I can only go the opposite way w/o the hassle! Both my old CAA and IAA ATPLs are time-expired and my only licence is the FAA one......sigh