To be a return of contribution, a distribution of the excess must be accompanied by any investment gain or loss attributable to the amount being returned. The regular distribution that you requested does not accomplish this and, therefore, does not constitute a return of contribution before the due date of your tax return.
There are two possible ways to handle this. The first is the most straightforward. Because the distribution of the 2021 excess occurred in 2022, you can treat the distribution as not having occurred by the due date of your 2021 tax return by filing a 2021 Form 5329 showing a $360 penalty and a 2022 Form 5329 showing that the regular distribution of $6,000 corrects the excess. The $6,000 will be nontaxable. Assuming that this is a nonqualified distribution, it will be made nontaxable by reporting it on Form 8606 Part III.
The second option might be to treat the Form 1099-R as erroneous and submit one or two substitute Forms 1099-R depending on whether there was an attributable gain or loss. If there was a gain, you would need to calculate the gain rate and split the $6,000 into part returned contribution and part gain, leaving some amount of excess in the account subject to penalty on 2021, 2022 and 2023 Forms 1099-R but avoiding the penalty on the majority of the original excess. In 2024 you would need to take a regular distribution after the due date of the 2021 tax return to eliminate the remaining excess and avoid another penalty for 2024. If there was instead an investment a loss, you would have to submit two substitute Forms 1099-R, one showing the loss adjusted amount as a return of contribution and the remainder as a regular distribution.
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