you fly on the temporary airman certificate if doing an FAA PPL, so no need to wait for issue.
You most definitely do not need a JAA PPL to fly a G reg, an FAA PPL is perfectly ok. Again, do not listen to sales people, check it in the regs (LASORS) in the UK, which are similar to JAA FCL and then print the relevant paragraph and rub it under the nose of whoever you want to rent from and thinks an FAA licence is not enough. (there are certain limitations, but not for VFR PPL flying within UK airspace, so they do not concern you).
good luck with whatever you decide to do! IP