Thanks for all of your suggestions and apologies for not having replied sooner; at some point Sky logged me out of here, so my replies weren't being sent and, of course, I couldn't log back in. The fact that I'm writing this is therefore a good sign....
A lot's happened since yesterday morning and I came across information elsewhere of varying quality, so I'll do my best to respond to your points as best I can whilst trying to keep it concise and with the caveat that my situation is perhaps a little more unusual compared to most others. Still a lengthy read I'm afraid, but who knows what might prove useful to somebody somewhere.
First, my solution: whilst in conversation with a very helpful lady at Sky, at one point she seemed to be about to ask me if I knew anyone with a UK no., before being distracted by a different idea. After all else had failed I suddenly remembered this, asked my son, had the code sent to him, he sent it to me, hey presto. Obviously this is only a temporary fix, despite the fact that he doesn't mind doing it indefinitely, but I've arranged to source a UK PAYG sim-card to register a UK no. with Sky and have codes sent there. Fingers crossed.
Once able to sign in I was given a recovery code to use if I ever can't access my phone, the point here being that I never received one when I was switched to 2FA, presumably because I didn't initiate it. Despite the fact that the Sky lady believed 2FA could be turned off via my account settings, it appears not; the relevant info in MySky doesn't show this option, but there is an FAQ asking if 2FA has to be used - the response is that Sky is rolling this out across all its services for our security, so seemingly "yes".
My conversation with Sky: with my Sky account closed when I moved abroad and an obsolete mobile number, that e-mail adress is my only link to them and everything she tried eventually led back to my old phone number. When she traced my old account via address, I couldn't complete the security vetting without either that mobile number, a Sky account or a Q box.
In the course of the discussion, she suggested that if she was able to remove the 2FA, it might only last for 6 months but - in view of my situation - possibly permanently, but that I would be advised either way. On Google AI (via this platform) it is suggested that if Sky do manually override it, for security purposes, it would take 21 days to regain access.
During that discussion, I also discovered that the access codes were being sent to an old alternative gmail address (presumably used for recovery purposes, but not an account I use often). Having said that, Sky did say they were sending the codes to my Sky address and - having assumed that I didn't get them because I was locked-out (although, at that point, I still had access to my account via the iPhone app) - I now know why I never got them there. In any event, when I did enter the code, Sky still wanted to send another one to that old mobile number, which begs the question as to why they would offer to send one to an e-mail address at all?
The lady's back office were telling her I needed to contact Yahoo, but apparently others on this platform have described this as a waste of time. She also said that I would get a follow-up message sent to my overseas number to see how things are going, to which I could then respond. Haven't had that yet, but it would open up another line of communication if necessary.
Other things my wife and I thought of at various times: i) Yahoo Mail Desktop App - unfortunately, log-in navigates you to the same Sky/Yahoo sign-in page as before. ii) Using a third-party mail service to bolt Yahoo mail onto - that would need sign-in to Yahoo Mail to obtain a 16-digit code. iii) E-mail forwarding - would need to have a paid version of Yahoo Mail. iv) Apparently Sky can be contacted via Instagram and Facebook and, had I hit a complete dead-end, it appears that Sky do respond to Trustpilot reviews.
If I remember anything else that might be of value, I'll post again.
