Safe mode is the only way I can actually get to use the iMac, but only under all of the conditions I have mentioned before!
Great, that was exactly the right question to ask. In safe mode, your iMac skips over loading the device driver for your video card. Contrary to some posts here, your iMac *can* function without that driver, quite well in fact; the buffering in that case is done in software, rather than hardware, so it's slower but plenty good enough unless you're a gamer.
So you could just boot into safe mode every time, but that carries the disadvantage that about two dozen other device drivers (like the ones that handle Wifi and sound) are also not loaded. What you want to do, then, is arrange for your system to boot with all its device drivers *except* for the video one. For step-by-step details, go here:
https://forums.macrumors.com/showthread.php?p=20621409#post20621409