As the second monitor behaves as expected if Windows is booted in Safe Mode, pretty much the first thing we tried was to boot Windows at 800x600

A piece of information you failed to share up to this point, rather leading to the chase of wild geese.

What we need to do is find out which of these drivers are disabled in Safe Mode, and then disable the same one in normal bootup. Except it seems impossible to actually keep any of them disabled.

The vaio's own switcher is done at hardware level, requires no drivers, and meets your needs (cloning). I'd suggest you uninstall the nvidia bits, disable the second display in the windows settings and go from there.