Definitely, I would get a 18" x 18" piece of black coroplast from the dealer or HD, sign shop, etc and then carefully cut a 3 sided 12" x 12" hole (flap) in the belly. Make sure the hole is on center in line where the dump valve handle is. That is where the dump valve or low point of the tank should be located. Then take a peak with a light and see what is happening when the tank is filled. There are straps under most tanks and yours may be loose or non existent.
Sealing up the hole is no big deal, close up the flap, Mount the coroplast share centered over the flap using 3/4" self tappers and then seal edges with gorilla tape. It will never come loose and some day you will need to service or replace the gray tank valve anyway.