I would do the latter if it makes sense for you as that exclusion is permanent and you will never have to pay taxes on that $250k, vs possibole multiple 1031s.  

Since then, I have been an avid listener of the podcast and became a free member of BP last October.Between then and now, my wife and I introduced our first child into the world, and we are currently in the process of moving to San Antonio permanently.

Or will it be a permanent dwelling?

They are not designed to be permanent financing options.  

My agent said that she’s going to negotiate a clause in my contract with the selling agent and the builder to permanently allow short term rentals regardless of what transpires with the formation of the new HOA.

If it's planned to be a permanent or semi-long term relationship than you can document various exit strategies as well for dissolving the entity. 

I'm currently a medical professional traveler, so I don't have a place to live permanently yet and am going to be moving to different cities/states over the next year at least 2-3 more times.  

While new construction homes won't create permanent jobs, we are able to get "indirect" jobs from construction spend to count.

It's nice option for little down, plus if your credit is less worthy, but that PMI is permanent until you refi on an FHA.  

If you see this as a permanent relocation it may be in your best interest to get a short term rental when you first arrive, even if just for a few months, while you look for employment and get to know the area.