Stalls when changing orientation can be from too little fuel, too much fuel, or loss of spark. you can sometimes tell which by the way it cuts out and more often by how it restarts.
- if it kinda fades away it is a fuel issue. If it is sharp "off" it would likely be ignition.
- Too little fuel you'd need to crank a bit, pump the gas, maybe more than once to restart. That would suggest blockage or restriction, or maybe low float.
- Too much fuel and it would seem flooded and may take extended cranking to restart. That may point to float too high.
- Spark cutting out could be a frayed or loose wire in the low voltage side of the ignition, moving with gravity as the car points downhill. A bad motor mount could allow the motor to shift and do the same thing by moving or stressing ignition wiring. Car should start right up, like nothing is wrong, once back in normal level ground.
- There could be other scenarios someone else here may be familiar with.