TSA and Immigration
As another Brit that owns a flight school in the USA (California) the regulations surrounding the TSA rules and visa requirements are slowly becoming clearer and thus enforced through cross checking by the TSA and also now examiners. Firstly TSA clearance is required for the Private, Instrument and Multi Engine, (Not commercial unless it's an initial Multi rating as well or adding a night rating). If you already have a private licence and have it foreign licence verified by the FAA then you do not need TSA clearance to fly. The TSA have started checking our paperwork to ensure that the student is legal in the country and also they are starting to check the type of visa verses the type of training. Also the examiners (one in particular) is checking and copying the visa and passport as part of the check ride paperwork.
The TSA process in the USA is now very efficient, we do the whole registration process on arrival and obtain TSA clearance normally within two days. Also the M1 visa issue is becoming a lot smoother as student visa's are now given priority above all other types of visa. I know that the USA system looks daunting but believe me in most cases it's an incredibly straight forward process. Basically if you need training other than recurrent training you need to go to a school that offers M1 visas, period, and there are pleanty of us around.