Also, my wife paid a joint filing online under my SSN, and the system couldn't figure that out
It's not surprising the system couldn't figure that out. There is no such thing as a joint-filing under a single SSN. You need to include both spouse's SSNs or ITINs on the 1040 to file jointly, and the return is treated as a "joint" return (meaning, equally by both spouses).
We did include both, but we either had to make an account under one of our names, or the check had a name that didn't match on another spot (it was quite a while ago). Despite the IRS having our filing records, they couldn't match it to the payment. It's really not a hard problem.
The check doesn't have to match either name, since names are not what the IRS uses to match payments to returns. The check simply has to have the SSN (or ITIN) of at least one of the joint filers.
It's really not a hard problem.
It's actually an extremely hard problem if you try to match payments by name, since there are a lot of people with the same exact name, many of whom even live in the same state or same city. Most checks don't include an address, and even those that do don't always match the address the taxpayer gave on the return.
It sounds like you failed to include your SSN on the check, which means this problem was one of your own making. That being said, if you could provide proof that payment was timely sent and the check details (check #, account, etc.), the IRS can match the payment received and will void penalties and interest that were assessed.
They weren't. The account had the SSN. The payment came under the other SSN. The filing was joint with both of our SSNs through the accountant. The agent I finally got on the phone after days confirmed that the problem was some mismatch between SSNs in the account, check, or filing.
Of course it was cleared up, but the point is that at least one of our SSNs was on everything. That should be a trivially easy for record merging or linking.
It's not surprising the system couldn't figure that out. There is no such thing as a joint-filing under a single SSN. You need to include both spouse's SSNs or ITINs on the 1040 to file jointly, and the return is treated as a "joint" return (meaning, equally by both spouses).