Hi Rob, I'm not really 100% sure on what exactly these large aviation schools can do for you, but I guess they work on the principle that if they can stream you into a job after "graduation" then they can charge high fees.
This is a sound model but if you don't have the right to work in the US, then it won't work for you as they can't (won't) employ you unless you get lucky and find one willing to sponsor a visa. There are loads of threads on this very topic and I think that the chances of that happening are almost zero.
If you just want to get your FAA certificates and try your luck in JAA land then I think you're going to struggle without loads of hours or a bizjet rating. If you are keen to try (and nothing ventured, nothing gained I suppose) then I would suggest doing it as CHEAPLY as possible as I think it is highly unlikely that you will be any more marketable with A CPL/IR from a large school than from a small one. I just think you'll struggle to get work whichever school you use so to minimise the risk I would do it on the cheap in case it doesn't work out for you and you waste loads of money.
FAA training is prety cheap compared to JAA and I would just look for a nice small school with plenty of aeroplanes. Most US schools can offer training for the CPL and IR as well as all the PPL stuff.
I once revalidated my FAA PPL with a guy at Denham. He was instructing (I believe) just on FAA certificates so that might be a way to get some hours over here. I guess there are quite a few PPLs operating solely on an FAA licence so they will need BFRs etc.
Anyway, good luck with it if you decide to proceed. It will be a tougher road for you than most I guess but I wish you well!!