How to change my home insurance with my mortgage company?

My payment was roughly $750/month (Interest, escrow, principle, everything) which pays for the home insurance as well.

Recently, my payment was bumped up to $901 a month. When I called, they said my homeowners insurance went up, and they suggested finding a new company, because the rates i'm paying are high compared to normal rates in my area. (Something like that)

I have car insurance through Progressive, and love them, so I went with them for homeowners insurance as well, as all the rates I called about were very minimal payment differences, plus I would get a bundle discount. The actual insurance is through a 3rd party company, and they are useless. I had a shower leak that messed up the wall and studs, and after 2 months of back and fourth calls and coming out to take photos, they told me they don't cover water damage or some fancy term they used. Paying out the ***, for a joke of insurance.

What do I need to do to find a new insurance company, just find a bunch of them and call? What info do I need, and if I find a better rate, how do I swap with my mortgage company? (Wells Fargo)

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