@sebastian-roth That makes sense. These new machines do also support BIOS, but they default to UEFI. Thank you for giving the path to that config file, I will look there next.
I did make a discovery just now. I thought exit to hard drive type (EFI) in the FOG configuration was set to rEFInd, but it was set to Exit. I changed it to rEFInd_EFI and my new public computers are working properly. They first boot to the network, the FOG menu, then after the timeout it boots straight to Windows. So the new computers using a fresh UEFI image are booting properly.
Now I am looking into the new staff computers, which are using an image that came from a BIOS install. I’m really trying to avoid having to reload Windows and copy data and reinstall programs. If it comes down to it, that’s what I’ll do though. They boot just fine if you bypass the network boot, but now they land on a rEFInd “about” screen where you can press enter and shutdown or restart the machine. Sounds like these computers do have some sort of a legacy BIOS fallback mechanism like you said which is allowing them to boot.