I am getting told many carriers do not want to write policies in Harris county while we had no hurricanes or floods or anything in last 5 years.

I do not have experience with 360 insurance and to be honest I have never heard of them, but with so many carriers out there that doesn't mean it's a bad company. 

@Jorge Leon I can send you some insurance carriers we use for our Chicago investors.In regards to the "80% coverage", I believe they were referring to 80% Coinsurance. 

Depending on how much more money is needed and x,y,z the insurance carrier may want to send out the adjuster to come and inspect the property.  

You’ll likely run into carriers that won’t like you making small claims, thus harder to get coverage in future.

(This would have stopped the fire you had, so it shows you're learning from the situation.)Doing those things allows your broker to present a case to carriers that you're going to be less of a risk now that you've had a loss.  

In the meantime they want me to file a claim with my insurance carrier when I owned the building for the recent damages

I would suggest getting estimates from a couple contractors familiar with fire repairs and comparing those with the estimate from your insurance carrier.

Since they are public numbers theres absolutely no protection for us from fraud.When submitting my accord for proof of insurance that goes directly from carrier to customer, not through my hands, unfortunately people have committed fraud with that number too.

I spend a lot of time trying to help them get their carrier started and time is money so I think that is a far way to start out.