We have a single HVAC system that heats/cools the entire home.

Austin area seems like a cool techie area with good rental demand.  

VERY cool strategy and progression story.

That's cool.

Using LVP was a smart choice—it holds up well when wet and is cost-effective to replace.

As a result, we have significant water damage to the floor and rugs in that 2nd floor bathroom and a bedroom, plus there is even more significant damage to ceilings, walls, furniture, and rugs to 2 bedrooms on the first floor.Our initial goal is to dry as much water as possible with wet-vacs and dehumidifiers.

First the obvious, look for wet areas around all of the pipes.

Here is one piece of advice When looking at areas to invest in check out this website https://www.areavibes.com/ its pretty cool it gives you a total livability score and rating for that areaBest of luck!

The main house is original (this place was built in 1924, very cool) and we rent it for $1,650/month.

Together we owned 330 units in Chattanooga (before it was cool) and did extremely well there.