So here's the follow up...
I drained about 1/3 of the pool and re-filled it, which brought my CYA down to around 60. Then I did another chlorine test, this time diluting the pool water with 3 parts distilled water and got a FC reading of 48 (!!) and a CC of 0, so I guess I had sufficiently chlorinated the water prior to the refill (and then some). I've spent the past week vacuuming, brushing, skimming, and filtering the pool and I'm happy to report that the water is now crystal clear. My current test readings are:
FC = 14
CC = 0
TC = 14
pH = 7.6
TA = 90
CH = 300
CYA = 60
I haven't added any chorine since the refill, and it's dropping about 6 ppm per day (with the help of some afternoon rain showers).
My original concern was that the water was still cloudy even after I was pretty sure I had shocked the pool properly. Looks like I just needed to brush and filter for about a week to clear all the dead algae that was clouding the water.
Thanks for the help.