If you can do some work yourself, you really only need to be able to cover the materials for those jobs.I aim to keep around $20k-$25k in cash on hand for unexpected repairs on 9 houses and two 2 families.

Best policy going forward...no good deed ever goes unpunished.

I find a combination of it being much easier to buy (30 settlements vs 1 settlement), manage (30 different addresses vs 1 building, 30 insurance policies vs 1 policy, 30 spring roof inspections vs 1 roof...), and yes, economies of scale ($850/yr insurance on my SFH vs $7k on the building) makes Multis more attractive to me than all SFHs.  

Or is their still some sort of "public policy" or law that would put them on the hook for this?

I always shoot first and aim later with my offers.The lease does not survive the transfer of the deed unless you want it too (I believe).

Our homeowner's policies are for those two home's as well as our personal home.

It's easier to buy a good umbrella policy (which you should have any how).

But you need to make sure you are complying with the NH requirements.If you have a mortgage on it, the due on sale clause will be a bigger issue, because you will need to switch to business insurance (your current insurance won't insure you if you own in an LLC), and the mortgage company will be notified of the new insurance policy with a different named insured.  

Some of which include:Debt ServiceInsurance (proper STR insurance - not a standard fire policy)Taxes (both normal property and STR taxes)VacancyCAPEXElectricity, Cable, InternetFurnitureSheets, towels, etcCleaning/maintenance Gardening/lawn-care Etc.Im sure I missed a few - but you get the point.

is there an insurance policy for that?