My best guess Alex is that this is a Fannie Mae guideline. We all have a ton of different Loan officers we use, but just about every one of them just service the loans to Fannie. I do have a correspondent lender I use for a lot of tough loans, and if there is anyone that can get around this it would be them.
One thing you can do is try going to the bank no one has ever heard about. Every city has them, and these banks don't advertise on google (or usually at all). A lot of "Community Trust" kinda names. They are basically small regional banks that potentially service their own loans and keep them on the books instead of servicing them and just selling to Fannie. Investors use them a ton for commercial loans, and that would be a route I would research quite a bit.
If neither of the above options work then your Fiance can look at a rent-to-own option for 1-2 years. Contract for Deed financing needs to be 10% down, but I have rent-to-own properties right now in your price range for $5,000 down. This is a seller financing program where the banks regulations do not come into play, so in other words if you have the DP and income you will qualify.
This is in my realm, and I can tell you that a lot of self-employed contact me or ones in this scenario. It is absolutely brutal right now getting a residential loan for this group of people.
I always find it funny that realtors complain about tight lending standards, but we are quick to disqualify and judge buyers who do not fit the correct standards of bank lending. Why should it matter if your finance was self employed previously or in college? If he has strong current W'2's and feels that the job is stable you are an excellent candidate.
But really it is not our job as realtors to judge because we are not loan officers, nor do we provide any type of financing for you. We are also not CPA's or certified financial planners. It is none of my business to be disclosed your financial information. My job is real estate and helping people buy and sell homes ethically.
Only you know if financially you are prepared to take on home ownership. Chances are you are currently renting and have an idea of where your monthly payment needs to be.
There is a path to home-ownership if you are motivated enough and willing to not take no for an answer.