Signature block is updated for the TF-100 test kit which I’ve used so far primarily for CH and CYA. I have a basic DPD test kit from the pool store that uses the same reagents for TA and pH so am using that up, along with the DPD tester just to see if I even have chlorine staying in the water while I get the CYA to something above zero.
Latest test numbers this afternoon were:
pH 7.5
TA 140
CH 250
FC 1
CYA 20 or less
After testing I added muriatic acid (7.0 target, Pool Math app calculations) to bring the TA down some more and have the aerator on 24/7 to bring the pH back up so I can repeat the process until the TA is at least down to 100. I also added a half gallon of 12% bleach and another pound of stabilizer (three total since the refill) and will check the CYA in the morning.
The tablets are history other than for vacation periods - liquid diet from here on unless/until we go with a salt system. I’m also looking at soft water options for the fill system, whether an RV type or tapping into the household water.
Of course, we just got a bunch of rain from a monsoon thunderstorm so that probably won’t help me figure out what changed because of me and what changed because of the rain - like I needed a confounding variable in the middle of all of this.
I’m interested in the salt cell approach but I need to get a lot smarter on them to even be able to ask an intelligent question about it. More reading for tomorrow…
You're doing great. Keep that FC up. It's better to overshoot a little on that. You can safely swim in a pool with FC at SLAM level, so a few extra FC points to fight off that AZ sun is going to be perfectly fine. You don't want to get into trouble with algae, so play it safe until you're more confident about how much chlorine your pool is consuming a day, and so how much to add each day.
Run TA and CH tests on your fill water. That will help you (and us) strategize. If you have high CH in your fill, you can leave your current CH as is, as it will accumulate fast enough from all the refilling you're doing to keep up with the AZ evaporation. Let that happen until you decide about the softener. I connected my pool's auto-filler to my home's water softener, and that has worked great. I have a small family, so the softener can keep up with us and the pool's needs no problem. YMMV. If you can rangle a hose from a soft water spigot to fill your pool, you might try that out first before you make any permanent connection or buy a separate unit. See if your softener can keep up. If it can, then that's one less thing to buy and manage. Mine regen's every few days. Not quite sure of the frequency, but I know it's not every day. So that means it's keeping up with demand. I only fill it with salt a few times a year, so that's ezpz. But hold off on that until refilling from your existing fill source brings your CH up to where you want it. Might as well let that happen for free!
Sounds good on the TA plan. That'll help stabilize the pH, too.
Regarding LSI v CSI, that's up to you. I'm not even sure how different those numbers would be. If it were me, I'd calculate CSI (Pool Math does that automatically), and then I'd calculate LSI, and see how off they are from each other. If close enough, I'd target a CSI as close to zero as possible (assuming LSI would also be near zero), and then just use CSI (because Pool Math makes that easy). See what I mean? Don't stress the difference. If I remember my "learnin's," LSI was originally developed for monitoring deposits in concrete pipes used by some industry (can't remember). Something like that. CSI is a modification of the same math, developed to be more appropriate for pools. I bet
@JoyfulNoise would be able to fill in my blanks on all that.
Regarding SoDel's advice about PebbleTec and LSI and TDS and PTI and A-B-C, as-simple-as-Do-re-mi, etc, not sure what all that means!

And something about an "Orenda app?" I don't know what that is. He's found a system that works for him. Everyone here does the same. So I'll just share what has worked for me (and what
I recommend):
When I first moved in to this house with a pool, I got into mixing and matching pool maintenance advice from multiple sources: pool guy, pool store, online, and of course my own logic about it. That just didn't work. It wasn't until I settled on TFP and ignored all others that my pool righted itself. I learned early on to pick
one source of advice, and stick with that. Mixing and matching just didn't work. And I certainly wouldn't mix and match pool chemical calculators. TFP's has been very carefully vetted over hundreds of thousands of pools, over many years. That's good enough for me... and it's all in one place.