Issues with account recovery of old Apple ID

Back in the early days of the iPhone, I lived in the USA and set up e.g. (not this) a fbloggs@mac.com Apple ID. A few years later, I returned to the UK, and had to have a new Apple ID, for which I mainly used my own email address, backed by a fredbloggs@icloud.com email address.

My only use for the fbloggs@mac.com Apple ID is as an email - it's set up as the backup email on quite a few services I use.

My current situation is that my Mac is happily using the fbloggs@mac.com email, and I'm receiving emails there. Both my iPhone and my iPad's Settings are saying "Some account services require you to login again." I'd also like to be able to get the email on my iPhone and iPad.

When I initially tried this, I thought I knew the password to this account, but it was wrong. So I'm now trying to do account recovery on this Apple ID. As well as having access to its email on the Mac, I know the phone number associated with it, which is my current iPhone (also associated with my current Apple ID).

Each time I try this process, I'm told I will get a phone call on a specific date at a specific time. But I never do. Today, on my 5th or so support call, I was told that this is because my phone or my iPad accesses the fbloggs@mac.com servers, which then decided that the whole process might be fraudulent and coming from someone other than me, as the real devices do have access to it.

BUT NEITHER OF THEM ARE LOGGED IN.

So I'm in the position where two devices that I cannot login with (my whole issue) are stopping the reset process by accessing servers. But surely they can't be logged into them, so - why, why, why? The only solution the support person could tell me was to switch off all my devices for the whole 6 day waiting period. How is this possible? I work on the computer and the iPad, and the phone is my only phone.

Is there no way out of this horrible mess? I'd happily delete the old Apple ID, except that apparently I have to be logged in to the account to do that.