Suggestion: In this situation, as in so many others, I recommend
a building-block approach. In other words, do warm-up exercises
in preparation for the main event.
In particular, note the contrast:
A) Using a tennis ball (or coin) atop a basketball has its advantages,
including simplicity and an obviously counterintuitive result.
B) Other geometries are easier to control and easier to analyze.
What I would like to see, but haven't yet found, is the "snowman"
geometry, i.e. small + medium + large balls. Let the small and
medium balls dangle at rest, and then whack them with the large
ball. Investigate the two cases:
-- initially touching
-- initially separated by a tiny amount