So when you say your MAX quits, does it totally turn off the power as soon as you move the switch, or are you saying after the bowls empty it runs out of gas and dies?
From what you are describing it sounds like your engine kill switch is the problem.
When the "Fuel" switch is pushed to the right, it is under the "ON", which means the Fuel is in the On position.
When the switch is pushed to the left it is under the "RES", which means the the Fuel is in REServe position.
When your fuel level runs below the resistor in the fuel tank the resistor is exposed to air and the temperature trips the relay that turns the fuel pump off.
When you move the Fuel switch to REServe it bypasses the resistor that turns the fuel pump relay off, thus allowing the fuel pump relay to come back on.
So even if the Fuel switch wasn't working properly, the engine should still run UNTIL the fuel bowls empty.
SO maybe if the kill switch has some corrosion in it, it's losing contact when you move the the Fuel Switch.