I don't know of any studies other than the limited
video Bob and I did. ...
I was told a long time ago that Predator did tests of efficiency of shafts/tips using their robot, Iron Willie. I think that was primarily aimed at developing break cues. I don't know what tests they've done recently, but some qualitative results are at
https://www.predatorcues.com/shafts/predator-low-deflection-shaft/ for energy transfer.
An earlier test was done by A.D. Moore, an engineering professor at the University of Michigan, in 1941. He hit a ball with a cue stick in a setup where both were hanging on wires. The height the ball swung up compared to the height the cue stick started at gave the efficiency of the hit (he calls it the coefficient of restitution) after some calculation. From Moore's manuscript:
... At any rate, the writer experimentally determined e for the case
in hand. The set-up was made and the readings were taken in one
afternoon (11-25-1941). The simplicity of the set-up, the ease of
making observations, and the accuracy secured indicate that someone
could, without much effort, add greatly to our list of coefficients.
The cue and ivory ball were hung by light steel wires beneath a
horizontal 10-inch board. String was wrapped around the ball, and
held in place with Scotch tape. Loops in the string permitted two
wires to be attached. The wires went to screw-eyes put in the edges
of the board, across from each other. Similar pairs of wires (two
pairs) suspended the cue for direct central impact, The vertical
radii were all 20 inches. When both bodies were at rest, they grazingly
touched.
The writer's brass-jointed cue was used. Its length is 57.5
inches ...
The result was that Moore measured a value of e of 0.81 or 81% for his equipment.
Moore's experiment suggests a somewhat more controlled test than the one Dave and I did. Suspend a stick as Moore describes but have it hit a very heavy smooth object (block of iron? concrete wall?) and see how far it swings back. The target does not have to be a ball to get a good measurement.