SoCal, do you have official information or a quote from some verifyable source that says that if you're doing flight training following the JAA syllabus, that you do NOT require TSA clearance, but if you do FAA training, you do?
Because, when *I* went there (year and a half ago) for my JAA PPL, *I* needed a TSA clearance. And if I check the flightschoolcandidates website, the only thing it says is:
"Category 3
o Candidates who request training for aircraft with a maximum certificated takeoff weight of 12,500 pounds or less.
"
No mention of the word FAA or JAA. And I would suspect that the TSA would not want to make that distinction anyway, since this is an anti-terrorist thing above all else. If JAA students were exempt, that would be a big loophole for the likes of the 9/11 terrorists, wouldn't it?
Other than that, your advice is very sound: if you only want to build hours towards the PPL, but not do the PPL skills test in the US, make sure beforehand that either the UK and the US school you're using have a standing agreement (like Cabair and OFT, I suppose, have) or let your local instructor contact the school to arrange something.
If you're only going to be hour building, make sure you negotiate with the school some sort of pay as you go scheme. When I arrived for my PPL they made me put down the whole (estimated) amount of money for the whole PPL in one go. I purposely paid a part of this by credit card, despite the 2% uplift they charged me, so that the credit card company would be on my side in case of problems.
If you intend to do solos in the US, I don't think you would need to have one JAA exam done, because you'll be flying those solos on an FAA student pilot license and all they require is a very simple 17-question exam on a few specific things with regards to solo flight (not in class B airspace for instance) and the local environment. But you do need that FAA student pilot license and, guess what, that is your FAA class 3 medical. Yes, you do need to visit a qualified US doctor, pee in the pot and do a few other simple things (and pay the 100 USD) to get an FAA class 3 medical before you're allowed to fly solo. They don't recognise a JAA class 2 medical there.