A higher pH is actually beneficial to killing the algae (there is less disinfecting chlorine, but the algae cells take it in more at the higher pH), though it shouldn't go above 8.0 or your pH test kit limit. So yes, you may need to add some acid during this high chlorine period and you'll have to keep the chlorine high so will have to continue to add chlorine (let us know the chlorine usage, especially overnight, as this will be an indicator of how much is getting used to kill the algae). You shouldn't need to keep adding acid once you've got the pH where you want it.
After the algae is killed and the chlorine maintains its level overnight, then you will let the chlorine level drop (get broken down from sunlight during the day) and you'll need to add base (Borax) during this process, especially if your pH gets down to 7.0 or your pH test kit limit.
It is not terrible if you just ignore the above advice and just keep the chlorine high with whatever its high pH is, but it might take even more chlorine to kill this algae under such conditions.
I'm a bit disturbed by your inconsistent pH readings. It's difficult to accurately measure the pH when there is a lot of chlorine (> 10 ppm) since the indicator will turn dark purple above a pH of 6.6 and this can be misinterpreted as a dark red so that you think the pH is higher than it really is. You could add some drops (2-4 drops) of sodium thiosulfate (the same stuff you add at the start of the TA test) and then test the pH, but the thiosulfate breakdown of chlorine is an alkaline process so will generate a false high pH reading (but you can just subtract about 0.1 pH from your measured pH for every 2 drops of thiosulfate as an approximation). If you happen to have "acid demand" drops, then you can try adding these after you take a reading to see which direction the color goes. Try the "acid demand" drops and see if the colors change from the high pH red to the low pH yellow.
Richard
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