An update to this increasingly pathetic situation.
While my formal complaint relating to the problems covered in my OP was upheld by the AA, the best they could manage in compensation was to offer to waive their extortionate £25 admin fee for updating some inconsequential changes in my personal details they'd picked up in our phone conversations
After their litany of serious failings I found this minimal gesture somewhat offensive and hollow so pushed them further and they eventually offered to refund abour 20% of my premium. I figured I'd get no more out of them and tbh was totally sick of wasting my time arguing, so accepted it and moved on.
Yesterday I called them at about half three to get a quote for changing my policy to cover a vehicle I was looking to purchase (as per
this thread). I made it clear that I was viewing it later that day and that were I to buy it, I'd call at that point to confirm my desire to change my policy to cover said vehicle subject to the agreements made on that afternoon's phone conversation. The guy on the other end of the phone confirmed that this change would incur no admin fee nor additional payment to my premium, asked when I'd be viewing the car and confirmed his understanding by stating something along the lines of "if you do buy it just give us a call and we'll switch the cover to that vehicle".
I viewed and subsequently bought the car. I called the AA at 7pm. I got a recorded message telling me that due to Covid their lines were only open 8am-6pm and to call back within these hours

This left me stranded with no way of insuring the vehicle amid zero prior warning of their reduced service - either during the eons of recorded tripe their customers are required to sit through whenever they call, or even on the part of the guy who took my call. Checking their website / previous emails they do make reference to early closure; but two hours later at 8pm
Having thankfully got the car back home without further incident I called the AA again this morning to implement the policy changes I'd been denied last night. Yet again the goalposts were shifted; the very apologetic representative mentioning the lack of any instructions to waive the admin fee for changing my car (as had been confirmed by one of his colleagues in light of the one it replaced being written off) and also alluded to an addition payment due of £20ish on my premium
Needless to say I refused to give them another penny, I'm now finally "covered" (for all the actual use it is) and another complaint has been submitted.
Tbh I'm actually lost for words as to how universally abysmal and shambolic this ongoing experience with AA has so far been - having wasted hours of my time with their consistant ineptitude and spectacular inability to provide the service I'm paying them for. Once I've had a response to this latest complaint I'll be summarising this in a message to the insurance ombudsman as it seems the "service" they offer is fundamentally unfit for purpose.