Since writing about the NUC’s problems installing Debian and Kubuntu in UEFI mode, I discovered the computer has a legacy boot setting which is essentially BIOS boot so with that turned on and UEFI turned on there was no installation problem. Kubuntu was installed successfully first, then I overwrote the installation with Debian-KDE and then put the kde-full package on to complete the installation.
So I now have two computers running KDE. The others will follow in due course but not urgently, just whenever they are next reinstalled. Once again as previously described the settings were put into X11 to handle the screen’s 1360×768 resolution and it has worked perfectly. Since I have two screens of this type on mediapc the issue is with the detection of the screen as 1920×1080 by default and 1360×768 not being one of the default resolutions provided in Xorg as implemented in many distros.
I can’t really be bothered working on the obvious efibootmgr problem as it will probably take weeks due to the voluntary nature of much of the maintenance of much of these packages. It would be OK if I had a spare system and apparently this issue is not unknown. But right now I can just use the BIOS mode because I am never going to need UEFI on this computer. I don’t use it now on the only other computer in the house that has its capability.