The tank is "skinny" in the up hill/down hill direction. So that is not your problem. As Bill says, maybe the pump is weak. Maybe a filter is partially clogged, etc.
I'm trying to relate the 1/2 tank syndrome while knowing that the fuel level is not the problem. Only thing I can think of is: as the tank level goes down, it tries to draw a vacuum. If your gas cap is no longer venting, the tank will draw a vacuum against the flow/fuel pump and starve the carb. Notice any noise when taking cap off? Next time going up hill and it stalls. Take cap off and try it.
