Get the FAA licences while you are there. FAA CPL ASEL/AMEL, INSTRUMENT AIRPLANE.
If you then need to go to an EASA CPL/IR, you only need an abbreviated course for the IR (typically 15 hours in the UK), and, I believe but am not sure, training as required for the CPL (worst case 15 hours - full course for IR holders).
With the flying in the US being much cheaper, it might even cost the same as doing the CPL/IR in western Europe, so you effectively get both FAA and EASA tickets for the same price...
Just make sure your visa status is ok for the training, also you will need TSA approval for the IR and the ME rating (but not for the CPL). Unless you are a US citizen or green card holder, that is.