I just told them that I am having problems with my payment didn't go through and looking for alternatives. So basically I let them decide what to do next, but probably that "looking for alternatives" was what triggered them to call me and ask my credit card number. By the way, this method was also successful for one of my client, few months before this.

Thanks for information about driver license requirement for paying in app.However, I finally got my membership extended by using the classic method:Being frustated with all the failures.Contacting Apple support through website as you mentioned, promised 1-2 business days reply through e-mailWait for more than 2 business days and got replied "Hi, I'm K; will contact you by phone, please provide details and time slots"I gave time slots for about upcoming 5 days and block my calendar on those time slotsWait for more than 5 days with no phone calls and no e-mail replySuddenly this morning got a phone call from a landline number "Hi, I'm C; K is not available so I am replacing her. Please provide your credit card number so I can manually order it"I gave her the exact card details as what I provided in the website (that failed).Waited a couple of hours; credit card charged; membership extended; all less than 24 hoursIn conclusion, I think their customer support is overwhelmed by this problem; so we just have to be extra patience waiting for response.Note for step 7 above: I was being paranoid at first because a random person claiming from Apple suddenly phoned me, asking my credit card number (and I explicitly said that to C). However, I gave it a go because she mentioned the name of her colleague "K" which is only possible if she really was from Apple. I think it's a good idea too to be sure that the phone call was really from Apple not from someone trying to trick you; just in case.Good luck!

I wonder if anyone tried paying through the Apple Developer app (for your iPhone in App Store)? I infer from one Apple's webpage that it pays through in-app purchase. I also always fail paying through regular method, but all my purchases through App Store were successful (music, app, etc); so it sounds promising.I cannot try it now since my membership has not expired yet so the button to pay in app is blocked.(Note: I am posting another reply with same topic but with more details, but still in moderation. Likely because I put some URLs there)