The goal would be to try to ascertain the amount of coverage that is needed for my insurance policies.

A well set Policy Packet should be part of the Lease.. in language... per Policy Packet.As well as addendum for Crime Free / Drug Free,  Lead Addendum, Pet, Security Deposit Agreement, move in condition check in sheet. to mention a few. 

Your homeowners policy should include coverage for a named storm which means if a storm is categorized as "Hurricane Sandy" then you have coverage.

Does anyone know how long it generally takes before insurance companies get back to writing policies?

Some banks and lenders are okay with money out of a HELOC for the DP but not for the PITI reserves required which is typically (3-6 months) but that goes off of loan size.But my question would be why would you want to take out a HELOC if you can do a cash out refinance. 

However, the brokerage has decided they do not want to go against MLS policy and not disclose the price.  

Yes, I would want to know about that.Start by asking the policy for what situations trigger an update to you the landlord.  

If they are VERY professional, they will have their processes in writing as verification that policies are enforced equally and fairly by their entire staff.6.

I already have an umbrella policy so not sure if upping that premium or moving it into any sort of trust/land trust or something else would be a smart move. 

If indeed it was the properties spoken of as 50% then Bill's suggestion will solve that as well as making sure that the surviving person is the beneficiary of the insurance policy along with a power of attorney for the business affairs in the case of death or other incopasitating injury.