I don't use a sling. I trained to shoot with a slitghly open hand, relaxed fingers. The bowgrip is finding its own way in my hand and all i do it make sure it does the same thing everytime. My bows dont jump out of my hand, not even shooting from a treestand down.
However, if your bow wants to jump out i strongly suggest you do something to avoid it from falling.
Try to find a way to make the movement the same everytime and adjust your gear to it.
Good luck.