Ideas on what's causing my click/tick/rattle noise?

You've got an '82 hydraulic head with early mechanical valve gear- did the stock '82 head use exhaust valve rotators?

I have no idea, and I didn't know there was such a thing as a valve rotator. How would I figure that out?

Easy check of the valve train.
Warm up engine. Remove valve cover. Put some rag around the engine to collect the oil. Wear gloves.
Start the engine, idling, put your finger on each rocker. If the sound changes you have found the culprit.

Excellent suggestion, I'll give this a whirl. I have quite the chore list going, it's a good thing I have the next few days off to work on this. Updates coming after I go get greasy for a while.