PeterD - sure it can be done. Thousands of airline pilots have got there, after all.
But, out of about 20-30 who (IIRC) started in that Flyer group about 2 years ago,
I think there are around 6 or 7 of us that have finished so far
that is an astonishingly poor success rate and reflects the collective hassle involved.
The FAA material can be wholly self studied. No "school" to go to.
The FAA training can be done by any freelance FAA CFI/CFII. No "professional school" to go to.
The FAA training can be done at any airfield. No need to travel to Bournemouth, Cranfield, Cambridge, etc, just because you have to be at these places to learn the airway routes which the CAA examiners always use. I would bet the majority of UK pilots would have to do hotel residence to get the JAA IR, even though there is a perfectly good airfield down the road.
The FAA instrument training can be done under the hood. No need for CAA approved screens.
The FAA instrument training can be done in VMC i.e. OCAS. Only the 250nm x/c flight needs to be (in Europe) in the Eurocontrol airways system. The JAA IR is trained in the airways but they still somehow amazingly manage to fail to teach people how to plan and execute a real flight in real weather on real Eurocontrol routes from say Lydd to Corfu.
The FAA exams are just one for PPL, one for IR, one for CPL, one for ATPL. You can sit them in several places in Europe (Flight Safety in Farnborough do them, I think). The CAA ones must be done at Gatwick, on the CAA exam timetable. The JAA exams are 7 for the PPL, 7 for the PPL/IR, 14 for the CPL/IR. The JAA ATP is not achievable due to the MCC time.
The plane you train in can be your own. No need for CAA-approved screens.
All previous training, from anywhere in the world, counts. So you can get a standalone FAA PPL in just a few hours' additional training, using your old JAA logbook entries. (Got to watch the FAA night requirements though). JAA licenses/ratings allow zero, zilch from previous training/experience. (Exception: ICAO PPL to JAA PPL conversion; the 100-hr partial concession).
Finally, the cost of doing a JAA PPL/IR in the UK, especially an ME PPL/IR, could be 2x to 3x higher than doing the same in the USA. Just look at self fly hire rates on piston twins, at the professional schools over here. Put that together with the FAA allowing previous instrument time (most UK pilots going FAA are previously UK PPL/IMC) and you will be looking at doing 55hrs here for just the IR, versus say 25hrs (previous instrument competence assumed) in FAA-land for the whole PPL/IR. The cost difference is huge.
What is not so bad is doing a JAA PPL/IR if one already has the FAA IR. The 50/55hrs flight requirement shrinks to 15 and the mandatory classroom attendance goes away. A lot of that Flyer group were doing just that - yet most still seem to have dropped out.
There are also effective strategies for the JAA exams. You get hold of a copy of the question bank, revise a bit, sit the 9 exams at Gatwick in one session, see which you failed, and revise thoroughly just for those and sit one more session. The absence of an oral exam in JAA is what makes this possible; most of the crap can be safely forgotten.
Anyway, it's all been written before
But it's horses for courses. The FAA route is very much for high time high currency owner pilots. Not worth doing otherwise.