There's another option, which is to obtain a standalone FAA licence, rather than a "piggyback" licence under 61.75.
Most, if not all, of your UK/European hours can be credited towards a standalone FAA licence, and a lot of the prep work can be done in the UK.
More info here -
FAA PPL/IR
UK Flight School conducting FAA training -
FAA Training - Courses Bonus Aviation Limited
I've not actually followed the above route or flown with Bonus Aviation, but have been thinking about this route and it's been discussed on other forums I read.