Would the IRS allow them to benefit from a 1031 Exchange if they would be "swapping" a million-dollar rental for one that is much lower in price?

Basically, there's no free lunch when it comes to taxes.Depreciating property lowers your tax basis.

Then the prices lower towards the date and you end up booking at a low price or worse just being vacant.I think manually pricing your STR'S is a much better approach.So many people are looking for the next cool software app to buy a subscription to.

Secondary markets like Greensboro, Winston, and Fayetteville will likely still be under the 1% rule, but our property taxes are lower than most northern states so the CoC (which is what you should be as/more concerned about) return will be favorable.

The house is in Woodforest though so rentability might be lower as well increasing vacancy risk due to high rental costs. 

I would negotiate a price point that is lower - maybe the 10-12% range above "market".

Markets like Texas (San Antonio or Dallas) or North Carolina (Charlotte) could offer better cash flow with lower costs.

Shortly after the crash my tenants learned that condo developers were renting out luxury apartments in the area for around the same rents I was charging so I was forced to lower rents. 1200/apt 2 1050/apt3. 

Most lower priced condo projects are not very healthy and why they are low priced.

I invest primarily in a lower cost area but also own property in, and am looking in, a higher cost area.