Determining Market Rents in a rural area

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I'm struggling with determining market rents in my area, and I'd appreciate some suggestions.

My situation:
All SFRs in small town (pop. 2100) in southern Missouri
The usual resources in my area don't apply. Rentometer, Craigslist, Trulia, Zillow, etc. have zero rental information for my market. My only online resource is HUD's Fair Market Rent. The problem with that is that it includes utilities and I have no idea how much they are allowing for that. Also, it is based solely on the number of bedrooms, and does not take into consideration any of the unit's amenities such as number of baths, square footage of the house, is there a garage, etc.

There is a constant demand for rentals in my market. We get 4 or 5 calls every week from people looking for a rental. A majority of those would probably be rejected by us for one reason or another, but it shows that the demand is there.

There is currently one house for rent in a less desirable area, and it is falling apart. No others are available in my market, so I can't call to inquire about their rates.

Most of the landlords are very small-time. They own one or two houses, owe nothing, and figure they've made a profit if they bring in more than their taxes and insurance costs. I don't really care for their opinion on rental rates, so I won't be having conversations with them about it.

We know how much rent we need to get to make a decent profit on any given house, but I'd like to be able to figure what we should be getting, based on the market. 

Suggestions, anyone?