Should I start the lowering TA process?

I would suggest simply adding enough muriatic to lower your pH to 7.2-7.4. That will reduce your TA as well.

Then wait a few days and check pH and TA again...repeat in a few days.

If your pH has not risen back up to 7.8 after a week, I would suggest to simply continue lowering pH as necessary and leave the TA alone.
 
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