I hope to secure an FHA loan to finance this and rent out the other two units.

A. they have to like you, B. they have to be confident in your ability to perform (buy) which comes from you showing them that you know the market where the property is located, and you understand the property type.

They have to hold money in reserves for non-performing notes that they can not lend out. it decimates their bottom line so unless they have to,they won’t.

First you've got to drill into what the performance of that property will be. 

The house rents for $850/mo, and I think I could push it to $950, give or take - but the debt payments (30-year loan at 4.75 or 5%) and taxes and insurance would take up all of that, leaving nothing for renovations.One alternative I’ve pondered would be to secure it and then seller-finance it to an owner-occupant.

I believe the damages will be more than the security deposit.

I believe the damages will be more than the security deposit.

If they pre-pay last month's rent and a security deposit equal to another month's rent, I think they have strong incentive to not bail in 6 months. 

I hope that you have changed the locks and secured your property to prevent anyone else with a key to return.

My partner and I are looking for a hard money loan right now secure a property and it’s minor updating.