I also have a 15,000 gallon plaster pool with very hard water and high alkalinity. Hard and alkaline tend to go together, but it's the alkalinity that affects pH.

I add one cup (8 ounces) of muriatic acid each day to hold the pH steady at 7.4, so one gallon (128 ounces) lasts two weeks. Same as your experience just dosed differently.

I know that bleach is very basic, so it tends to push pH higher, but I don't know if a chlorine generator does that. Also, I've seen that chemically adjusted water pH will tend to lose the adjustment over time, so water with a high pH that is chemically adjusted to a lower level will trend back upward. Dunno why.