@injaneb, thanks you put me on the right track! In my case there were 2 extra steps:

The extra EFI was not on the C disk but on the J disk (the target of the backup) which was an external USB. I...

Device Manager, Mice, rightclick on HID-compliant, power Management,
uncheck "allow this device to wake the computer"

(I'm not 100% sure on this but this worked a few months ago. Fans came...