In general, the large financial institutions and major banks tend to have less flexibility for non-traditional lending due to the need to standardize their product offerings. If by chance you bank with a local financial institution such as Hinsdale Bank and Trust or the local Northern Trust office, then they have greater flexibility to make a loan which would not fit into a cookie-cutter loan program. This is quite common that local banks, who generally keep your mortgage on their books, are more willing to work with you than large banks who don't keep your mortgage (they sell it off, so by nature they need to standardize the mortgages they offer). Our firm works with a number of local lending institutions who actually know the name of their customers and may be a good referral for you if you are interested.
One potential upside opportunity, if you are a private banking client of a small or large bank (meaning you are have more assets / money at their bank), they will also step out of the normal lending guidelines to work with you.
Good Luck in your pursuit of a larger home,
PahRoo Appraisal & Consultancy
I can't lend in you home state, but I'm sure some others will post here shortly that might be able to assist.