Somewhere in the neighborhood of 1/2 gallon of muriatic acid should neutralize the pH increase of 8 lbs of borax. I would start with a pint and keep adding a pint at a time and restesting until the pH is in range....then add your baking soda to rasie the TA and then retest the pH and adjust. You need to do this over a few days time. Don't try and do it all at once!

And yes, rain can lower the TA!