Even within the same company different offices may have different policies.  

Went through the LLC battle in my head several hundred times, and ultimately landed on an umbrella insurance policy as the band aid to hold over my liability anxiety.  

What is your late rent policy?

Depending on your loan type, you will need to ask your lender if anything will prevent financing, if so those repairs will need to be done prior to closing - example roof needs replacing, poly pipes, wood rot, etc. 

Thought this might also benefit you.1st pillar is avoiding unnecessary and risky activities (don't drink and drive, insurance generally won’t cover your poor decisions) and take good care of your investments - these simple steps will help you prevent lawsuits before they even occur.2nd pillar is a good insurance policy as that cover the majority of your exposure.

Prior to the walk through, we put together a list of 20 questions for the seller and their agent. 

I am looking for an alternative to my current landlord policies for 5 houses.

Should we just keep everything under our names and get an umbrella policy instead?

The 'welcome' idea is a very good one, and your prior landlord CLEARLY left an impression since you acknowledge that it "was a nice touch."

It’s hard to tell if this is true from the information you provided, but safer is always better.Call the title company to see if your lenders title policy should be modified.