Best way to request a manual reconciliation after my refund was withheld for a balance that I also mailed in a check to pay?

I have a double payment issue. My refund was offset for a balance, but I also mailed a check for that same balance which has now cleared my bank. I need to request a refund for the overpayment. Seems like the IRS system often operates on a delay, so it likely processed the refund withholding before it registered my mailed check. Will they eventually catch it? Should I continue to try to contact them during the busy season or wait it out then contact them in a few weeks?