It takes 4 weeks for the TFL compliance and exemption database to update, if it's going to update.
Hence TFL have a manual registration process for your sort of situation.
See the website here.Successfully register the car as compliant and the charges will stop.
Officially they'll want a copy of the Certificate of Conformity for the car and a copy of the current V5c. Some manufacturers will let you have the cert for free and some will charge. And it may take a while to get. If the vehicle was new at first registration then the cert might be in the dealer documents.
You can try sending a copy of the old V5c for the car that shows it's original registration and a copy of the new the V5c that shows the new private registration. And a covering letter. TFL should be able to see from the copy V5cs that both registrations are for the same car as they will have the same VIN number. Also demand a refund of the erroneously levied charges.
I wouldn't try deleting the car from Autopay until this is sorted. If you do so then your wife will start to get PCNs.