My bank's underwriter/loan officer actually said to get the best rate with them to specifically setup an account with them (They aren't my day to day bank) and just use it for my house payment. For the past decade the only transactions it has ever seen has been the direct deposit and the auto-withdraw for the mortgage.

Really? Both times I got a loan they wanted bank statements from all of my main accounts and verifiable income history, but they didn’t care that I was paying from an account that I had just opened for the specific purpose of paying the loan.