I would look at options to do UK and EASA in parallel, I think they'll exist before too long, as schools are shopping around for licencing authorities, as you'll be far from the only person to want that option. Your priority however is to do it in the UK if that is the only place you have rights to work.
Once you have an EASA (or UK) CPL, converting to FAA is easy - took me half a dozen hours of learning how to fly "the FAA way" (they have a lot of funny manoeuvres that the rest of the world doesn't include) then one written exam and a checkride. Going the other way will be a pain, as the written exam load in Europe is much heavier than in the USA.
If you have an ICAO IR and sufficient hours (Europe it's 50hrs PiC IFR, in the USA more complex but similar) you can present for the IR skilltest / checkride either side of the Atlantic without any mandatory training and only the one written in the USA (none in Europe), although will need to put the study hours in for the two relevant regulatory regimes as both will put you through a strenuous oral on all that.
Incidentally, I got too busy to pursue this myself, but there is definitely work in the UK for people who can instruct in the FAA system, for the various people who need flight reviews and the like. How much work, I'm less sure, but more than none.
(UK, EASA and US CPL/IR, mostly done the hard way, but with a bit of system gaming to minimise the exam loads)