Usually they want to see the return and the proof of filing ... the return doesn't need to actually be processed.
See if the mortgage company will accept a paper return with your ink signature on it along with the filing history report and/or the email you got for acceptance. Your return's electronic filing status history records all e-filing activity related to the return, including the Electronic Postmark is part of the PDF you can download.
Since they cashed your check maybe a copy of the cancelled check with the signed return will work.
Or get the ACCOUNT TRANSCRIPT from the IRS also showing the payment.
