However, if you bought it and managed it as a market rate apartment, your experience would be very different.My point is, I can control how fast a unit turns simply by adjusting my asking rents.  

This isn't a lending requirement but have some boots on the ground other than just the construction company.

Can you carry the property for the construction period?

Nobody likes living in a construction site.Keep on keeping on and find some hybrid strategy that ticks your boxes.

I actually work with a great team in LR that offers turnkey and new construction.

Hello I'm Whitney Steadman a plumbing contractor who looking to do some investing and  fix&flips Have a strong construction side eager to learn more of the investing side and property acquisition

Would it be more expensive to buy an older property like this vs buying a new construction in TX? 

Had several challenges with their bookkeeping after I had to make an adjustment to one of my monthly payments.

Just be sure to check local zoning rules, manage construction costs, and explore financing options like HELOCs or DSCR loans.

I do see many investors incorporating a similar strategy with new construction builds, heavy rehabs, or in instances where the property was bought far below market value (usually a wholesale type transaction).