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pH and TA cannot be changed individually without effecting the other (except one way I'll explain).
Having a lower TA will help keep your pH more stable. Muriatic Acid will lower your TA and Lower your pH. If you use pool math, you can go to the menu and choose "Effects of Adding." That will show you what happens when you add XX amount of acid.
If you use Borax Mule Team 20, or Soda Ash/Washing soda to then get your pH back up, it will also raise TA. It is a zero sum game. You will be back where you started.
You should read this-->
Lower Total Alkalinity
The simple answer is that you should add enough MA to reduce pH to 7.0 and Aerate. When the pH goes back up to 7.4, add acid again and aerate. Do this cycle until your TA gets to about 70. May take several days. I built one of the suggested aerators on top of a sump pump. Took me about 4 days to get TA down from 140 to 70. Now I'm good.
There are examples of Aerators in the link above. You can also google "pool aerator." The trick to having the aerator be super effective is to have it make LOTS OF SMALL BUBBLES. Aeration releases CO2 out of the pool raising pH. CO2 outgasses (is released) at the highest rate when pH is betwee 7.0 and 7.4. That is why you reduce pH to these levels.
This is what I built ... See Post #4.
DIY Aerator