More progress - in the hope that it will help anyone still interested!
I can now get FireFox (but not (yet) Safari) to work with a credit card.
It seems necessary, though, to be logged in before attempting a purchase; which is to say that pasting a URL into FireFox causes the transaction to fail.
If I mistakenly do that, I have to log out, clear the cookie(s) and log back in.
Otherwise I get into the loop described in my steps 7 to 14 from an earlier post.