Perhaps I’m paranoid and overly suspicious - perhaps he’s out of town, looking for properties, and he doesn’t have phone coverage.

Some will even allow AirDNA projections (usually with 25-30% down) as the rental income for DSCR (debt service coverage ratio)  for investment properties as qualifying income. 

Before I purchase an insurance policy I wanted to seek some guidance on the best way to proceed.I received 1 quote so far for a HO3 policy that has 600k+ of dwelling coverage, 70k of additional structure, 450k personal property, 200k loss of use, 500k liability, and a few extras like equipment breakdown, water backup, service line.

Is there a third-party company that offers Damage Protection coverage for midterm rentals?

Plan your route to maximize coverage.

I would get this out to quote with multiple Independent Agents (they represent multiple carriers) and if you can determine any agents that write a lot of apartments that would help also.The type of info you should gather that will help in the quoting process:1. current coverage. 

Hello,I was recently told that if I or my partner personally complete work on one of our flips that we own under and LLC that it voids the liability coverage within the LLC and we as individuals would open ourselves up to Liability.

The mortgage market is healthy so there are several ways for income to be calculated including but not limited too: full income verification of two years W-2's or tax returns, 1-2 years of a 1099, average deposits of 12-24 months of personal or (50%) of business bank statements, an up to date P&L, DSCR (debt service coverage ratio) or rental income (investment properties only). - Appraisal.

As you said, having 6 months of rent coverage Is extremely important.

As far as the other units most policies have "building and ordinance" clauses which proved some coverage if you have to update to "Code" but if the other units aren't damaged and are still up to code I wouldn't think there would be an extra coverage provided.I urge you to go into the process treating the insurance company as a partner not as their going to screw you no matter what :).