Exactly, on a .303, which has near nil recoil in the big picture, foam will stay in place. My guess is, this old gun will have a leather, steel, or plain wood butt. Putting plastic between you and it is a poor idea from a dental and facial aesthetics point of view.
Even on a .450-400 Nitro, a pipsqueek in comparison, foam's going to make the gun squirm under the recoil load, and you don't want that. Even poorly secured recoil pads can shear off the big nitros, let alone foam. All you want between you and a big gun is a well fitted shirt or shooting jacket that won't slip. You'll see most large calibre African guns have checkered butts, or in modern guns, grippy recoil pads. There's a reason... don't try putting foam in between.
For reference, your jungle carbine might recoil with an extremely mild 14 or 15 ft-lbs of recoil energy, and a recoil velocity of a touch over 11 fps or so. This 4 bore will likely generate
140 ft-lbs of recoil energy, and a recoil velocity of 20 fps or a hair more.
Ten times the recoil energy, and double the velocity (sharpness), which isn't bad for such a big gun, on par with a standard nitro express in recoil velocity. Lessons from a jungle carbine mean literally zilch in the big bore world, and after you shoot a nitro for the first time, your Lee Enfield will come into perspective. Heck, even .338 Win Mag, and .375 H&H start feeling light compared to the real magnums. It's all perspective.