You have me worried:
First add the Muriatic and record the pH (you don't need to record the TA) AFTER IT'S FULLY DISTRIBUTED.
Then start aerating until pH pass 7.2 to 7.3

The WHOLE KEY is that when you add the muriatic acid, and lower the pH to 7.0, it pulls the T/A down too. Then when you aerate it raises the pH back to 7.3 WITHOUT raising T/A again.