You can google the IRS and get a phone number to address it. But it may be easier to wait and file 2022 and treat it like a prior payment. In Illinois you can call and schedule an appointment to see an agent Near Downers grove off Butterfield RD.

We already have attempted a dozen times to call and also schedule appointments at an office in MN but everything leads to automated messages. We plan on reaching out to a tax firm to see what options we have; otherwise, we'll just use that amount as a pre-payment on the 2022 taxes.

You cannot use the 2021 overpayment as a payment towards your 2022 tax. Whatever the problem is with the refund of the overpayment, you have to deal with that as a separate issue. If you claim it as a payment on your 2022 tax return, the IRS will simply say that you did not make that payment, and they will bill you for that amount plus penalties and interest.

I'll tell you what has worked for me to reach the IRS.  And I'll follow that with information on how to reach the IRS Taxpayer Advocate Service to see if they will help you.

I have found that for me it was best to call the IRS just before closing time--about 6:50-6:55 PM and go through the steps below.  I figured a lot of folks would not call that close to closing, and that if I was one of the last to get into the queue, they would finish off all the people who were in the queue at closing time.   I still had to wait about 25-30 minutes.   

IRS:  800-829-1040 (7AM-7 PM local time) Monday-Friday

When calling the IRS do not choose the first choice re: "Refund", or it will send you to an automated phone line.

• First choose your language.  Then listen to each menu before making the selection.
• Then press 2 for "personal income tax".
• Then press 1 for "form, tax history, or payment".  
• Then press 3 "for all other questions."
• Then press 2 "for all other questions." 
• It may then ask for your SSN, but do not enter it.  Just wait.    If it asks for SSN a second time, still do not enter it.
• Then it will get "tired", and you'll get another menu.  Choose 2 for "personal".
• Then in the next menu choose 4 for "all other inquiries", and it should transfer you to an agent but expect a long wait.
• I usually use a speakerphone so I can work on something else while waiting.

If you have no luck reaching the IRS, or don't get satisfactory information, you can try contacting the IRS Taxpayer Advocate Service for your area.    They are especially prone to help if you have an economic hardship, or if there have been continued delays with lack of info from the IRS.    At the following IRS website, select your state from the dropdown menu, and it will give you the number of your IRS Taxpayer Advocate.    If the Taxpayer Advocate can't/won't help you, ask them to transfer you to an IRS agent.  A couple of users reported that at least for them, that was a backdoor route to the IRS.

http://www.irs.gov/uac/Contact-a-Local-Taxpayer-Advocate

Also see this article for more info on how the IRS Taxpayer Advocate Service works::
http://www.irs.gov/taxtopics/tc104.html

"We received a notice from the IRS for overpayment on a 2021 return;"

IRS does not roll this forward.

For 2022 tax return purposes it should be ignored.

Eventually, IRS operations will smooth out and you will get your refund, someday..

If you can show hardship, the TaxPayer Advocate Service may get involved.

P.S. I'm in the same boat - waiting for a promised check.