I will try your idea and let you know how it behavesAn automatic should never stall just because there's a hill. The car should know how to deal with it.
I would try to rule out a metered air leak or purge valve leak.
You can find the purge valve on top of the intake manifold with a vacuum hose that runs into the intake. Block off the lines/ports with a piece of plastic wrap and a rubber band and see how it runs.