The closing disclosure rules require that you disclose the “closing date”. In my opinion, you would need that date before you can make the disclosure. Also, if you implemented a procedure that consistently created inaccurate APR disclosures that needed to be re-disclosed, I believe examiners would likely take issue with it.
If the APR exceeds the allowable tolerance threshold in Reg Z you would need to re-disclose and wait 3 business days to close.
The APR tolerance is generally:
1/8 of 1 percent above or below the actual APR for regular transactions;
1/4 of 1 percent above or below the actual APR for irregular transaction;
and
There’s a couple of additional tolerances rules for mortgage loans to consider that are related to an incorrect finance charge. This over simplifies it, but if an incorrect APR is the result of an incorrect finance charge, where the finance charge is still considered accurate under Reg Z, the APR would also be considered accurate. (The APR tolerance standards are under 1026.22.)