Beefing up the mounting points won't work IMO.
The body is not rigid enough to hold the frame solid, and the frame isn't solid enough to hold the body straight.
Boxing the frame, or full cage, and additional/better crossmembers would greatly reduce the problem.
If you strengthen ONLY the body mount points, you will induce failure where the strengthening ends, such as the sheet metal that the mounts are welded to, or the frame, likely between the mounts.
I experienced this when switching from rubber to poly body mounts. Poly seemed to make the problem no better, if not worse, which if the body was rigid enough to keep the frame from flexing, would not have been the case. If anything, rubber lets the body move a bit more which allows the body to stay a hair more intact when flexing, while the frame takes more of the abuse.