72 Demon starts bogging sporadically once warm

Is it possible;
that when the car is not level the fuel pump sucks air at or in the tank. Since it runs continuously, the pump tries to fill the line with air and the pressure falls to zero. The engine still runs on whatever is in the bowls. When the car returns to being level, the pump once again fills the line with fuel and away you go.
But if the engine stalls before the line is filled,and you turn off the key, which turns off the pump; then there you sit with an empty filter.If this problem is worse as the fuel tank empties, then I think this is a possibility.
I have also seen it happen that the jumper to the pump from the sender sucks air under the clamp, and this also gets worse as the tank empties. When using gear-clamps, I always use two per end and stagger the screw heads as close to 180* as possible, cuz screw clamps tend to bunch up the hose at the screw heads, and do not properly grip the hose at the screwhead. It may look tight, but it almost never is. The factory spring-clamps work best.
But if the jumper is proven to be sealing, then I would drop the tank, remove the sender, and inspect the pick-up.