In focussing on the question as asked, I forgot to offer an alternative you may prefer.
But first, to be clear, the Roth limit is not a cutoff at 144k, it is phased in from 129k to 144k (for 2022; anyone finding this in a future year must use different numbers).
If your MAGI (for 2022) was under 129k, you could recharacterize your trad contribution as Roth. This can in general be done by moving the contribution plus allocable earnings to a different (Roth) account, but in your case since this account contains only contributions for one year you can recharacterize the whole account if the custodian supports that. Recharacterization is treated as if you originally made the contribution to Roth, and includes the earnings, unlike conversion (including backdoor) which treats them separately.
This would mean you can't take a deduction for 2022, so (just like the backdoor method) you need to amend again to remove it and pay back the refund you got for the deduction. You are supposed to complete a recharacterization by the filing date including any extension, and you didn't get an extension so that's April 18, but there is a procedure where you can do it up to the date to which you could have extended (Oct. 16), see pub 590A.
If you are between 129k and 144k, technically you could recharacterize as Roth the part that fits under the limit, and leave the rest in trad for tax year 2022, either converting it in 2023 or later, or simply keeping the trad (as I noted in my comment). But this would be more complicated even than making it nondeductible trad and converting it with reporting of the earnings, so I don't think it's a solution here.
Note the custodian(s) needs to handle a recharacterization specially in order to report it correctly and not put you at audit risk. Don't try to just move the money yourself; contact them or look on their website for specific instructions (perhaps a different form) to use for this case. (In contrast the custodian does not need to be informed about whether you treat a trad IRA contribution as deductible or not, although you need to report it on form 8606.)