Our application process is you fill out an application and pay the fee for credit and background check.If you have an eviction, or outstanding collections against you, we likely wont rent to you unless you. 

They’ve had a lot of success, the potential for a high ROI is outstanding.

I would just require documentation for the extra income, AND the outstanding debt that the husband is resposnible for. 

Your real estate has to be able to appraise for high enough over any currently outstanding debt(s) on/against it (that is called your “equity.”)

Are they a nationwide lender?

Before settling on Chicago, I searched nationwide and tried Texas, Indiana, and other areas.  

Typically, the Vendor will not want transfer a pro-rated amount for the outstanding rent - leaving us with the risk and effort to remedy the situation.  

That said, most of REI accountants who post here on BP serve clients remotely, nationwide. 

Getting clear title and clearing outstanding liens which you mention is the biggest one.

I'm sure there are plenty of statewide/nationwide area lenders that could do it for you.