Are the two halves of the clamp touching each other, or is there still daylight between them?
My Magma grill has a "lever" that's actually the "nut" on a stud on one half of that clamshell clamp. So it's easy to get it tight enough. Perhaps with Phillips screwdriver, getting it tight could be a problem.
Perhaps you can change the fasteners to get a better grip.
Maybe it's also possible to move the clamp to a vertical tube of your pushpit so that weight won't be able to rotate it.
I think butyl tape might tend to "flow" and not give you a solid lock-up.
I don't have a lot of confidence in our grill. With everything hanging off the back rail, a lost
dinner, grill, propane
cylinder, etc are just one failure away....