As a follow up, 3 days after the treatment I described, my results ended up as follows:

15ppm stabilizer
1.0ppm chlorine
7.2 pH
120 TA
190 CH

A few days later, we believed there was an odd smell from the pool, so I was told to shock the pool with 4 gallons of chlorine (I only had about 2.5) to deal with the potential smell (it turned out something happened to our towels, which is where the smell came from.)5 days later, I had my pool checked again and my TA and pH went up (150 and 7.6), while my stabilizer disappeared (0 ppm.)

I then treated the pool with 2 quarts of muriatic acid, but we had a huge rainstorm which caused me to drain the pool down a few inches (about 1200 gallons, if I'm calculating it correctly.) This is where someone new to the pool store started running tests for me, so I'm not 100% sure if these numbers are right:

0 stabilizer
0.5 chlorine
7.6 pH
100 TA
160 CH

Is that normal for TA to go down while pH stays the same? I'm currently in need of lowering pH while keeping TA the same, but I'm not sure how to accomplish this?