Unless you've got some strong base source such as plaster curing, then your pH rise really is coming from two main sources. The increased aeration such as from a spillover most certainly causes faster carbon dioxide outgassing and that causes the pH to rise. People with spillovers, fountains, waterfalls, etc. often find the pH rises more. However, lowering the TA does help, but 70 ppm isn't actually that low in this case. See this thread where pH stability was attained at a TA near 50 ppm.

The second source is possible chlorine gas outgassing. By any chance is the distance between your SWCG and the first pool return rather short? If so, then chlorine gas may not have a long enough time to dissolve in which case it can outgas from the pool and that would cause the pH to rise. If you have eyeball returns, you might try pointing them down, at least for the one closest to the SWCG.

Also note from this chart that a higher TA and a lower pH are way over-carbonated so if you are lowering your pH down to 7.2 instead of just to 7.5 or 7.6, then that could be part of the problem as well. If you are using full-strength Muriatic Acid (31.45% Hydrochloric Acid), then a half-gallon in 13,000 gallons with a TA of 65 and CYA of 80 would lower the pH from 7.8 to 6.8 which is way too low. Even with half-strength Muriatic Acid (15-16%), that would still get down to 7.2 which is too low. The pH will fairly rapidly come up from such low pH, but then slow down in its rise as the pH gets higher. Also, the full-strength acid addition would lower the TA by 17 ppm while the half-strength by about 8-9 ppm so you'd have to be adding baking soda regularly to prevent the TA from dropping (but you didn't mention that, so is that what you are doing?).

As for the sandstone flaking, only if your water was fairly aggressive would it dissolve and yes that would raise the pH, but also the CH level. Given your water parameters, your saturation index is probably OK at the higher pH, though too low soon after you add acid. You said you had very hard water, but what is your measured Calcium Hardness (CH) level? I figured it was probably around 500 ppm.

If you do end up letting your TA get lower to 50 ppm and if you don't try and lower the pH as much -- just lower it to 7.5 only and let it rise to 7.8 -- then you can consider using 50 ppm Borates in the pool which will provide additional pH buffering and also be a mild algaecide that may let you cut down your SWCG on-time if you happen to be fighting nascent algae growth. What is your current target Free Chlorine (FC) level with your 80 ppm CYA? If it's below 4 ppm, then that could be part of the problem since a higher SWCG on-time results in more hydrogen gas bubbles for more aeration and in potentially more chlorine gas outgassing as well.