He mentioned above that the fuel pump relay and pump were already replaced.

There's a check valve at the fuel pump that can stick and may cause intermittent trouble, or perhaps the fuel pick-up is gunked-up/clogged.

My brother had a car once where the windage baffles in the fuel tank broke loose and no longer kept the fuel from sloshing back and forth. When his tank was below about a third or a quarter his car would sometimes sputter or stall when cornering or braking as the fuel pick-up would momentarily not be submerged.
Does this only happen when the tank is low? Just a thought.