No room for the unexpected. 

More than likely, you’re going to encounter some kind of problem or unexpected circumstance at some point.

Another aspect of this is parasitical family members who are suddenly "close to you" and need accommodation because of some unexpected and horrible and unfair emergency. 

IMO cash flow provides a way to mitigate the risk of unexpected expenses and loss of income due to vacancies.

We have an insurance policy on the rental house (through State Farm), that includes a personal liability section, which is essentially equal to our current net worth.Given that a tenant could sue for more than this if an accident occurred, we are thinking about adding either LLC or an umbrella policy (or both) as extra protection.Any advice on which way to go, and if LLC, any recommendations for a law firm or company the Indianapolis area?

Sounds like a box of unexpected surprises, I'd pass.

If not, paying off the STR could leave you vulnerable to unexpected expenses or downturns.

They like extra room to avoid accidents, etc....Just my $0.02....

.- So, you may want to consider locking in an interest rate via a 2nd mortgage.Do you have reserves for unexpected expenses?

Set aside reserves for unexpected repairs or vacancies.