"We also made the mistake of not using the “Pay Sales Tax” feature to record payments.  Unlike the original question, we did use the “Sales Tax Payable” account in creating the payment, so the P&L for those years is correct."

Meaning your entry is not seen at all, but you bypassed the Function.

"The problem is that “Sales Tax Liability” summary is not correct in its detail."

Fix it any time you are ready to fix it, then.

"and am looking for the cleanest way to straighten it out."

Pay Sales Taxes properly, now, for each and every payment you made the Wrong way. Use that same date and check # and match the amount. Delete the Wrong Entries.

Now Banking has not changed; you replaced the wrong transaction Type with the right one, paralleling the exact info. You affected Cleared Status, so it is time to do a Mini-Rec or Interim Reconciliation.

Use the same Statement as just previously used and the ending date and balance. Ignore the beginning balance. It is the Net of all cleared transactions and you know why it is wrong. Ignore it. Clear only your Recreated transactions that you know were previously process by the bank and cleared previously. Bottom right, you see a difference of 0 and you are back on track.