Car stalls only after adding gas

How full are you adding gas? If you add more gas after the pump automatically shuts off, that could be the cause of your problem (theoretically).
My theory is that gasoline fumes, or raw gas, are going into the EVAP carbon canister; the EVAP purge valve is open (it shouldn’t be); the flood of gasoline fumes are being drawn into the engine and flooding it. Good theory, eh?