It sounds like there is something else causing the pH to rise other than carbon dioxide outgassing. If it is rising even using Trichlor pucks with the TA low, then something in or added to the pool is causing a pH rise. If for some reason the plaster were dissolving, then the calcium carbonate would cause the pH to rise. By any chance are you noticing a rise in Calcium Hardness (CH)? In Palm Springs you probably have a lot of evaporation and refill (unless you have a pool cover) so the CH will increase from whatever is in the fill water.
Also, with carbon dioxide outgassing, the pH rise will slow down as the pH gets higher, but your see it rise to 8.1 and beyond. This again points to something else causing the pH rise.
You did an acid wash in February so it's possible that leftover plaster dust could have the pH rise, but I would have expected all of that to dissolve a while ago. Or maybe you exposed lower levels of plaster with copious amounts of calcium hydroxide so that your plaster is "curing" though again I'd expect that rate to slow down over time. If this is the case, then you'd want your water to have a higher TA as with the bicarbonate start-up procedure and the pH not dropped as low as you have been doing.
I don't think you need to go below a TA of 50 ppm for any reason. You don't have water aeration features and it appears that your pH rise is from some other source.
If you have plaster dissolving adding more calcium carbonate to the water, then the lower TA would actually have the pH rise more quickly. With your current numbers with a TA of 40 ppm, then in 7300 gallons dissolving 4 ppm (1/4 pound) of calcium carbonate would cause a 0.3 rise in pH. If this were calcium hydroxide instead, then it would take half as much (1/8 pound) to cause a 0.3 rise in pH. However, I'd expect such dissolving to stop when the water is saturated.
Why don't you bring the TA up closer to 50 ppm or a little higher (not above 70 ppm) and see what happens with the pH when it's around 7.8 or so. See if the pH goes above 8 and how much and if it slows down at all at that point. It does seem like your acid wash has caused a situation similar to new pool plaster curing. That's my best guess at this point.