that's why evidence of married life isn't a requirement for AOS from K-1, because it is hard to get really anything in such a short time frame. we can't get my husband a bank account until he has a state id/drivers license, and we cant get that until we have at the very least an NOA1 from the AOS.
but I also agree, the notarized letter from FIL about your living situation would be good
also encourage just getting your own place together. depending on the landlord, whether its one person or a company, they should only need one person to meet whatever financial stuff they require. they didn't even need an SSN for my husband when I added him to the lease.