The full answer is there is no way to pay without a card tied to a US address, thus making Turbotax almost useless to people living abroad. You could keep waiting for TT to update their policy and let us get on with our lives, and you could also bang your head against a wall until you bleed out. TT doesn't care, won't be bothered to ever look into it, and will continue to ignore their customers so long as they get paid somehow.
So the best answer TT will ever offer is "You figure it out. Too bad, so sad"
The short answer is there is no easy way to pay from outside the US without a US billing address. The best I can recommend at this point would be potentially some form of prepaid card that is associated with a US address.