Re: adding the CYA (now that I've got some) how long do I need to wait after I've added muriatic acid to add the CYA? And can I continue adding muriatic acid to the pool (when recommended by Pool Math) even if the CYA hasn't yet fully dissolved in the skimmer?
When in doubt, wait about 15 minutes between adding different chemicals, with the pump running to circulate everything in. Not all chemicals needs this pause, but it doesn't hurt to wait and it's a good rule of thumb that's easy to remember.
As Marty points out, Muriatic and CYA acids get added using different methods, so you can do either while the other is going on. Regardless, you don't need to wait days between, I think that's what you were getting at. So if you've got CYA in a sock in front of one return, you can add your MA in front of a different return. Or if the CYA is all dissolved, and you're waiting a few days for it to show up on the CYA test, you can still add MA during that time.
Personally, I don't add CYA into the pool, only into the skimmer. Still in a sock, which I hang in the skimmer by trapping the end of the sock between the skimmer lid and the deck, so that the sock isn't laying in the bottom of the basket, and can't float out into the pool. It's sort'a hanging mid-skimmer-basket.
I burned my brand-new pebble with liquid CYA (don't use that stuff, however tempting), so I'm paranoid about having it over or in the pool. The granules are only slightly less "dangerous" in that regard, which is why I keep to the skimmer.
If you do add CYA into the skimmer, know that some of it will get trapped in the filter for a while, so it could take longer to show up on the CYA test. Also, until any that is trapped gets dissolved fully, you can't clean your filter, or you'll be washing out what CYA it's holding.
If you hang the sock in front of a return, be sure it is attached to something, such that it can't come loose and fall off and end up on the bottom. Be sure there are no holes in the sock through which granules could escape. And be sure the sock is not laying up against the side of the pool either. No touchie-touchie to anything, it needs to be suspended in the water. (You can see why I only use the skimmer for this, because, to me, it's too risky otherwise. Others have no problem doing it that way, so it's just a personal preference.)
Treat CYA as the acid that it is. Keep it off your deck. Keep it off your pool's finish. Handle and store it carefully and safely.