Mr F, try posting this in Private Flying, where there is regular debate as to whether or not training in the US is a good thing.
PPL in 3 weeks? Well, maybe, just maybe...... if you are sharp, focussed and have continuous luck with wx and aircraft, but I suggest that it might be unwise to believe in "guarantees" in this regard. No doubt you already appreciate that even if you could get a licence in 3 weeks the learning process would then be just beginning.
I looked at the US places but ended up doing the ppl in the UK (it took me 11 months). I do not regret my choice, but can see arguments both ways. Try the other forum to see what they are... Good luck, whatever you do.