I'm not sure how you would make an additional payment for 2024 without associating it with a Form 1040 or Form 1040-X. I think I would just file the Form 1040-X even though the original tax return might not have been processed by the time the IRS receives the Form 1040-X. The credit to your tax account will happen when they receive and process the payment, but it will likely take weeks to months to actually process the Form 1040-X, long enough for the original tax return to have been processed.
The only issue I can see is if the IRS detects underreporting of income and assesses the additional tax themselves. They might recognize that the additional amount has already been credited to your tax account and will only need to bill for interest.
