sounds like a problem with the fuel pickup in the tank. when you piont it up the hill the fuel might be getting away from the pickup, or there could be a rust hole in the pickup tube part way down that sucks air when the fuel moves away from it going up steep hills. have you tried it with a full tank ?

i had issues once with a ford sedan when i fitted fuel injection to the cleveland V8. couldnt work out why it kept cutting out going around long corners. until i realised it only did it if i had 1/4 of a tank or less, as the car was cornering the fuel moved to the side and exposed the fuel pickup letting air into the lines. with the fuel injection when there is no pressure in the lines the engine stops.

sounds like you have a long steep climb and after the carby runs out your stopping. have you tried it on a shorter hill up and down a few times . if you can do the same amount of climbing but broken with some down hill sections to allow the fuel system to refill then that should prove the pickup problem.

dave