It's very user friendly, free, and gives you coverage nationwide

So for those I use the American Water line coverage plan.

Yes LLC is a "coverage" by definition of a legal entity which is not you, and it doesn't matter if the liability is triggered by an STR guest, an LTR tenant or a handyman working there etc.

Furthermore, unless you set up the property insurance correctly, you could end up without coverage in the event of a claim if the property is deeded in the LLC and insured personally.Happy InvestingDerek Dombeck

These can be financed if a full remediation has been completed with the engineers report and insurance coverage can be bound.

I went to a broker to get new coverage, and one of the first questions asked was if it has asbestos siding. 

I'm trying to determine what coverage levels I really need to have.

To answer your question, Yes you can buy an umbrella policy that offers you only General Liability coverage on your properties and will be blanket coverage for all of your properties.

AND with an additional caveat: the PROVABLE cash flow from the property must service the debt with a cushion of at least 20 -25%, so a debt service coverage ratio of 1.2 - 1.25.That being said, the 'gap' can, in some cases, be filled by seller carrying back a second lien. 

Many title companies are run by lawyers who want to stick to title and not have to pay for malpractice coverage.