The purchase price, loan amount, your interest rate, whether you need mortgage insurance, your homeowner's insurance cost, property taxes, and your current monthly debt obligations all factor into your DTI.  

You will have mortgage insurance, but at least you'll be in a house with a low down payment. 

They reached out the next day and wanted to write and offer with me as their buyer's agent.

Here, the insurance has skyrocketed due to hurricanes, taxes are up, and the property values have increased faster than rents.

Lease-to-Own Options: Some sellers might offer a lease-to-own option where you rent the property with the intention of buying it after a set period.

Quote from @Mike Hern: Quote from @Erik Bergerud: Quote from @Nate Sanow: I haven’t yet but am actively offering that way.

We had a large insurance claim at one of our 1970s-built apartment complexes. 

Start there it will offer many more options and choices than the 'loan officer' at your bank branch.

Been rejected, beat by cash and higher offers a bunch of times.

Their job is to make 300 dials, talk to 30 people and have over the 5-6 people that are at least curious about an offer on their home.