If you're not getting any significant training, but you're just going to do some brush-up and then a flight exam, you might be exempted from TSA clearance
I think you'd find that you would require TSA clearance as there would be the PPL flight test with examiner.
The easiest route would be piggyback PPL. Once you have this, and before you leave the USA do the CPL flight test/oral/exam (as Backpacker mentions no TSA required), that is what I'd do anyway. When I went through the verification of authenticity process some years ago, it only took about 2 weeks, though this was a while ago I admit. When you pick up your licence at the FSDO they will "test" your engish - I think the guy said to me "you can speak english right?". IF you do the CPL flight test then by virtue of passing the check ride and oral with the examiner, they have examined your english speaking abilities.
Whichever way you go it would certainly be easier and cheaper than trying to keep a G reg flying in the USA.