I purchased 4 commercial rental buildings over the last 3-4 years and simply went with an agent that held some other types of insurances that I had (auto, homeowners, umbrella, etc).   

I do not set up separate LLCs for each property, primarily due to the requirements of my Umbrella insurance (they won't insure LLCs, only people). 

Typically, high-risk trades that are almost akin to gambling fall under the umbrella of speculation, whereas lower-risk investments based on fundamentals and analysis fall into the category of investing.

Just get an umbrella policy if your concerned.

Some others just use an umbrella policy because it covers them in a better way (legality) than LLCs, some others choose to have both LLC and an Umbrella policy.

I would get a STR policy and add an umbrella policy to cover any kind of catastrophic event.

I do have an umbrella policy for the properties owned personally. 

I do have a landlord/tenant policy and carry an umbrella - but the LLC is not a named insured.

One of the things you can do to protect yourself is get an umbrella policy. 

Try Allied and see what they say.One problem I have had is having my umbrella policy cover my LLC's but I guess that kind of makes sense given an LLC is technically a separate entity.