I'd say either go the full FAA route with a view to conversion, or do it in the UK - forget JAR approved IR schools in the states. This is becasue you WILL be flying to the FAA system, NOT the JAA system even though they are JAA approved. Its not the "flying by sole reference to the instruments" which will cost you extra hours during the conversion, but the different procedures between the two sides of the Atlantic.
Although OAT may offer a £3800 conversion, I was quoted £7500 at Bournemouth including the extra hours they anticipate you need. I tend not to trust prices that seem artificially low.
IF you go the FAA route, make sure you are trained by somone who knows the JAA system. For £13800 you can go from PPL to FAA CPL/IR AND JAA fATPL including conversions etc.....have a look at
www.usajar.co.uk
Cheers