"While the instructions to post as AR make sense, A/R is not an option in the account assignment when creating a refund receipt."
The point is to use AR on the Check "expense" because that overpayment already exists.
"Some posts have suggested deleting the refund receipt, but I need it to match up with the bank transactions."
Your Expense entry as a check will already do this.
You have to understand Two Conditions:
Either you Already have too much money from an Overpayment against AR as Payment;
Or, you are now issuing the refund from a Credit Memo as a refund, because you didn't already Owe them the money.
Two completely different scenarios and the point is not to do Both, for the same scenario. Once you have Negative AR, don't Also create a credit memo and refund, because while those two offset each other, you would still have negative AR from the overpayment or prior condition.
This applies to Any method of bookkeeping using AR.