The less obvious coverage I see often, is ACV over RC.

In NY, due-diligence title search has county and municipal searches which includes open permits, CoO and any outstanding county tax liens I think if you read the Conditions section of a title policy you'll find coverage is only for matters recorded in the public records which is probably defined in the Definition section of the policy as those records intended to impart construction knowledge to third parties. 

@Derrick Wortman   Debt service coverage ratio is the right product for you.

Replacement Cost coverage (RC) for building vs Actual Cash Value (depreciated).  

We created a comprehensive scope that didn't break the budget.

If your insurance coverage isn't enough, they could seize the LLC assets, but not your personal assets.Additional thoughts:1.

The correct coverage will depend on who will be occupying (owner/Tenant) and if anything is being done to the property (renovation).   

As for the qualifications, since you're mentioning commercial loans, this would be based primarily on factors such as the properties debt service coverage ratio (DSCR aka cash flow), the guarantors FICO, and the loan to value ratio. 

Talk with your insurance agent about coverage and getting an umbrella policy for liability.

If you get hurricane and flood coverage then the repairs are covered under that less your deductible