First, please recognize that there are always TWO approvals for a mortgage: One is for the borrower and One is for the property. It is quite feasible that one can be approved and the other denied. In the scenario you have laid out, on the surface I believe your fiance's income issue would be evaluated differently by another underwriter; however, the final outcome is in the details of the documentation. Since you mention you are putting 20% down, I assume you are applying (your fiance is) for convential financing. FHA views income more leniently and that may be an answer for you both. On the other hand, the challenge you have ;with the current lender may be surmountable....with a new lender. Once a lender has made up their mind on income, it is unlikely to get them to reverse the decision. I certainly would encourage you both to continue the course for obtaining a mortgage.
Now, the property in your given situation is an entirely different story. Unpermitted additions are, at times, the kiss of death for obtaining financing. Not always, but very often (MESSAGE to agents and consumers: Do NOT do work on a property without permits!!!! It is always an issue with financing). Sometimes, an inspection and certification from a licensed contractor will enable you to get a permit..."post construction". That is entirely up to the community building inspection department. Also, a underwriter MAY approve unpermitted work based upon certification that the work was "done in a workmanlike fashion and meets all health/safety and building code requirements". The latter far more likely for non-structural items.
I am curious to know if the unpermitted work was disclosed in the listing agreement. Did your agent know or disclose to you prior to offer? Just curious, because I probably would have recommended passing on the property until the seller had worked with the city/county to resolve the permitting issue. In other words, get the issue fixed before it ever becomes a financing issue.
That said, let me get back to a possible resolution. First, as I stated, it sounds like the income issue has some merit for success so I will start with that assumption. The real issue is the property. Do you have a copy of the appraisal? if so, the resolution to this situation is to get an underwriters assessment of if they can sign off on approval on the property and/or provide direction on what they would require to fix the permit issue. Not all lenders will review an appraisal without an application (most will not); however, I believe I could get an exception in this situation. In short, as much as I would like to represent you (and every borrower I can), i respect that the financing process is very frustrating....I would offer to overcome the largest obstacle prior to dealing with the lessor issue of income. Contact me via my profile if I can help.