No, do not mail another amended if the only problem is the payment. The IRS will process that and know that you are due a refund. The IRS cross checks stimulus paid, taxes paid, etc before it finalizes. They will see the correct amount you paid and adjust your amend to send you a refund.
Mailing in a paper return for them to open next year would be way too late and a waste of your time and theirs.
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