I say your goal (dreams with action steps and deadlines) of owning 1-3 Apt building is NOT outlandish.  

We have done very well turning "tight" margins into a profitable experience. 

Yes, it can be an challenge to meet meet the 45 day deadline in traditional real estate.

Usually flipping is a relatively risky strategy, but if inventory is tight it might be a good market for it. 

The East Nashville and Nations/West Nashville Market is tight.

Inland, maybe, but it will still be tight.

For the financing part, remember money market was tight, and they are more strict, that's what I found out early on.  

Are the margins too tight here?

Fanny and freddie sell millions of homes thru bulk sales and the few that filter down to the mls are retail priced in a tight market with low inventory and high demand Homes under 150k are very competitive because the mortgage payments are cheaper then most people rents . 

With 12 months left until the moving deadline, I would start this process now and if need be rent for a month or two or make arrangements with a new buyer (provided the Mortgagee allows it) to stay until the right time.