Welcome to BP Daniel, I did the same move from Seattle down here a few years back! 

Advice is for you to do this for another 5+ yrs to go through some real ups and downs to get a better sense of realized cash flows (net turnovers, evictions, capital events, etc). 

Basically do it in paper before you go down the road.  

Unlikely to be any tax due if this is your first gift, but it will count against your lifetime exclusion down the road. 

Can anyone help break this down?

Not only would it decrease your monthly mortgage but you'd be able to get into it with a very little down payment since you'd be living in one side of it. 

On the other hand, I’m hesitant to simply pay down more of a property, as we don’t need the immediate cash flow.Fortunately, both my wife’s job and mine are recession-proof, which allows us to be a bit more aggressive with our investments.I’d really appreciate advice from investors who have experience with frequent moves or military service.

I’m interested in how others evaluate and track down these kinds of properties, especially from a distance.For example:When looking at distressed properties in other states or cities, what are your main indicators that it’s worth pursuing?

Let's me put numbers to it: Bought a STR for $400K, 20% down, 8% DSCR loan.

That is IRS trying to narrow down the number of returns they need to mess with.