Thanks for the tips guys.
I'd be surprised if it were a flexibility issue. I can hit bottom without any rounding of the back, and I'm careful not to let my knees drift through the range of motion. Nor do I allow myself to relax at the bottom, as some make the mistake of doing.
It was once suggested to me that the issue might be ankle flexibility. My left ankle was busted pretty badly when I was a teenager, and it never regained a comfortable full range of motion. So I've tried putting plates under my heels, and that seemed to work at first. Helped keep my body more upright as well, instead of feeling like I was folding down into the bottom position.
As for the level of pain: I had to stop before I hit my 5th rep on the second set last night. Afterward it was bad enough that I couldn't even manage a single bodyweight squat. Today getting up from a chair is a tender affair, and managing stairs is less than comfortable.
Prior to this I've done wide stance squats to parallel, never having had them cause a problem with my knees -- even when I was loading up over 300 lbs for 15-20 reps. I've utilized front squats to finish my thighs off, and never had a problem with my knees then, so long as I warmed up carefully before hand.
For some reason, 200 has always been the magic number when it comes to my knees. If I go deep, my knees hit a danger zone around that weight.
I'm going to skip deadlifts on Friday, and see how my knee feels by next week. I can't stand the thought of slacking off in workouts just because of this, limiting myself to lighter weights... so maybe I'll do my warm-ups with the narrower stance, and then go wider as I increase the weight? Perhaps in that way increase the durability of my knees. Perhaps even use light front squats for a finishing set after.
I'll take a second look at the suggestions that have been made in this thread. I'm pretty pissed off about my knee crapping out on me at the moment, so a clear-headed second look will probably do me a world of good.