Obtaining a Mortgage Based on Job Offer Letter

i am finishing up my doctorate and have accepted a faculty position at a university in a different state. my new salary will be more than twice the current combined salary of my husband and i. i begin september 1st but we would like to move during the summer. so far, every bank we call says we can't get a mortgage until i have a pay stub. one bank said we can get a pre-approval with the job offer letter but can't close until i get my first paycheck. another said, maybe if we had 20% down. the only way we could have 20% down is if we liquidated all of our retirement accounts (including my mother's - who's living and moving with us). we do currently own a house that we are listing within the next 2 weeks but the real estate market is pretty bad here so we aren't too optimistic that it will sell quickly. we may end up renting it after we move if it doesn't sell. once i am working we will have plenty of income to cover the 2 mortgages. if we could get a mortgage on a new house before we sell our old house we'd have to use a small downpayment so we could keep some of the cash to pay for both mortgages. are there any plans out there that could help us? we are comfortable with borrowing some from our retirement accounts but don't want to borrow it all. we'd probably prefer a lower downpayment though, with the option to refinance in a year. i have very good credit as does my mother (who could potentially be a co-owner, but her income is small too). my husband has average credit. thank you.