The problem with that tack is that finding a new job might well take me over a year, just like it did last time.

Even still, I would start to search actively for a new job, AND I would wouldn't keep it a secret from my current employers. You could let it "slip" in conversations you have with your boss, so that he knows you aren't joking. If he truely values you, he'll give you the raise you deserve. If he doesn't, you can quit if/when you find a new job.
I doubt that your boss would fire you over this, seeing it's unlikely he'll find somebody else who will do your work for a less or equal amount of money. (like you said, you're underpaid as a Unix admin)