There would be no 2020 taxable amount: If this had been done right the first time, then you would be doing the amendment for 2020 due to the later repayment. That means there is no taxable amount afterall. There is no reason to make the amendment to 2020 resulting in taxable amount, then amend it again to meet the provision that it was repaid and there is no tax due. You can skip all of that extra part. Amend and report the 1099-R and that it is a full rollover.

"The distribution had fed/state tax withheld."

Was the Gross Distribution amount, the repaid amount? If so, you treat it as a full rollover: report the 1099-R and the repayment = net is 0. If not, it was not fully repaid. If not fully repaid (the gross), you have to report this as a partial rollover, and you will now have a three-year spread for the taxable amount.

Most times you want to indicate this is a coronavirus distribution to avoid the 10% penalty and to be able to take advantage of the disaster distribution provision(s) including the later repayment option. Your taxpayer took advantage of that repayment provision, so even if there would be no early distribution penalty, you need to indicate it is under the disaster provision.

"Change the distribution code on the amended return from a "1" to "G" so that it isn't included in taxable income and the taxpayer can get his withholding back?"

The distribution code is what the Issuer knows. It is not what the Taxpayer did with the funds. They didn't know if he was using, converting, would be repaying, etc. You don't make that change. You show it per the 1099-R; you show the rollover. No, he won't get back the withholding; you seem to consider withholding as Tax on the distribution. It's not. All withholdings and estimates are prepayments against likely total 1040 tax owed. Once an amount is paid in through withholding or estimates, it is just part of that tax year's payments.

The only way anyone gets anything back is if they paid in (or get credited) more than owed. You already stated the 1099-R was not even on the original filing. If there was a balance owed or a refund due, that ship has passed. Unless you are changing something that changes the bottom line of the 1040, there would be no further action as to refund or balance due. This entire concept and paragraph has nothing to do with the fact that a distribution had withholding. It has to do with the tax picture, not the payment taken by withholding.