Credit card?
Why do you say it is essential to pay with a credit card? Assuming one is following the first part of your advice and paying in arrears I can't see why one would need the insurance aspects of a credit card.
I personally pay for my lessons by credit card because the club lets me and I get points, but I don't see that paying by debit card would be that bad an idea, e.g. if the club kicked up a fuss about the fees. You're paying for the instructor/aircraft time that you've just used, so how would you ever have a claim that it wasn't delivered?
Certainly at my club paying afterwards is standard procedure - sometimes a while afterwards in my case as I've forgotten to pay once or twice!