If that isn't enough, you can try adding more brackets as well. If they are really heavy, you might just have to build proper supports that go to the ground.

What kind of insulation? If it's fiberglass or an open cell foam, rip and replace. If it's rock wool or closed cell, you can dry in place.

For the sheetrock, you will need to remove some to assess the damage behind anywhere you see signs of water damage and to allow it to dry better. Anything that has lost its integrity should be replaced as well. If you can stab through with a fork, replace it.

Outside of that, it's more about what else to remove to make repairs/drying easier. One large hole is easier than 5 small holes.

Also, get yourself a good stud finder that finds pipes and wires. It's way cheaper than the repairs you are looking at.