It would be, but I'm not in the UK, I don't know of any local instructors, but there is this guy I know who is planning on becoming a flight instructor, training in the USA, possible for him to be a FAA Instructor without having residency in the U.S., as that would make things different (Ability to train locally). But if he isn't able to be an FAA instructor then he would have to have an 8710 signed and whatnot. Correct?
If you put as much effort into getting the necessary Visa's and TSA clearance as you are putting into trying to find ways around getting them, you'd have them long ago
LOTS of people do this EVERY WEEK, go to the USA, do their three weeks training and come back with a PPL. Why so much effort into finding a way to avoid this?
If you can really afford to operate your own private jet (even a share is going to costs lots) then you can easily affort to sort out a PPL.
dp