You could always head to Jersey or the mainland for a few days and bang out a number of hours at somewhere like Old Sarum or Bournemouth? Happy to give you a lift to / from Alderney if you buy me a pasty at Alderney Airport
(I have friends there so always happy to visit)....
Last year one of our group did his entire PPL in 3 months of weekends and Friday afternoons at Bournemouth, from about June - Aug, so it is possible.
if they find that there is no visa and the student is taking flying lessons they will jump down hard and make life bad.
Not to bring this old one up again
but it is the word "Visa" that causes so much confusion. I await definitive proof that an M1 visa is required for flight training, if someone posts a link to the INS website that specifically says this then I will retract my statement and change my view