For the sake of posterity and future sohc4ers using the search feature, I'll explain what happened and how I screwed up.
The ticking noise was made much worse by a horribly misadjusted tappet. How did this tappet become horribly misadjusted when I claimed that I just "fixed" them? Well, I lost track of whether I was adjusting cylinder 1 or 4. Someone called in the middle of doing all this, and I failed to doublecheck that I was in fact adjusting the correct, i.e. loose tappet that supposed to be TDOC. I guess the lesson is, don't wrench when you're running late to work. Or don't have a job, one of the two.
Another lesson would be to never tighten tappet covers too much. Since I'd just replaced mine, I was able to remove them at work with small crescent wrench. In fact, the whole fix involved a small crescent wrench I found lying around and a box cutter blade as a screwdriver. Take that, MacGuyver.
There you go, Future People and 22 people who read this. Keep your tappets in shape. Don't do drugs, stay in school.