Calling the four main brackets 1,2,3,4 from the a/c shroud, you could add short ones fore and aft to join 2 and 3, and add two more to go from each side of the metal base of the air conditioning unit (that the shroud mounts to) to 1.
That would stiffen it all. To support it all in the middle from up and down motion, you could jam some wood under as mentioned above, and screw it to the brackets with a piece of carpet under the wood to protect the roof.
If it is like many Rvs the fridge sits on a plywood floor you can drill holes in to let the wires down to the space underneath which might have the power centre or a furnace or whatever. You can go sideways from there to go down to avoid any tanks.
Shade from that shroud could be a problem when the sun is low if you are not parked to avoid that.