It seemed pointless to use Time Machine since all my documents are synced with iCloud, and only recent instances are kept locally. Let me know if I'm wrong, but I assumed Time Machine wouldn't back up files only referenced on the drive.
I have another older Intel Mac with a drive large enough to keep all my documents on. It also syncs with my iCloud but keeps all my documents on the drive, not just recent ones. I have this Mac backed up to external drives using Time Machine. I only use this Mac for this purpose but only switch it on when I want to update the data on it and let it run its backup. Since it only gets switched on every week or so, it's not ideal, but if there's a better solution when my principal Mac doesn't have enough space to accommodate all my documents, I'd be interested to hear it.
I intended to get an M4 iMac (when they were released) with a 2TB HD, which will enable me to do back-ups directly from my principal Mac.
I'm not convinced about the failing display, though. Could a display really fail in such a way that the visual portion of the failure is restricted only to parts of the display that are showing the desktop at the time? The image below is simulated. I couldn't possibly grab a screenshot when the desktop goes black, but this is exactly how it looks when it does.