Computer attempts the same update on every shutdown

Sorry - I've been a little 'otherwise occupied!'

I can see no significant errors in the windowsupdate.log.
In the CBS.log, there are a lot of
"Info CBS Warning: Unrecognized packageExtended attribute."
errors

Unfortunately, I have no real idea what they mean Their placement follows no specific patterns that I can see, and I'm at a loos to work out what may be causing them, apart from registry problems.

I think your best bet is to attempt a Repair install first - and if that fails, then a clean install would be the only option.

See here for Repair Install instructions...
Repair Install

To ne honest it is in no way Microsoft's problem. It's corruption on your own system. MS with the best willin the world cannot legislate for that.