I tried different layouts, but this was the smallest I was able to come up with that visited all 4 stations sequentially and allowed the stations to be close enough to transfer the balls from one station to the next.
Below is a picture of where the rotating chassis connects to the main structure. It plugs right into the support tower in the original Akiyuki design.
I used old wheel hubs I had in my collection for the the shock absorber trip arm (wheel with split axle hole 3482). I tried other variants, but found that this was more reliable.
I had to change the gearing on the through-unit to slow it down. I added an 8:24 gear reduction right after the 24T gear that is driven by the train, I changed the 20:12 bevel gears to 12:12, and I changed the worm gear to a standard 2L worm driving a 24T gear. (I have disassembled it already, but I'll see if I can find a frame of a video which shows the gearing).
I originally used standard rechargeable batteries, but they would die very quickly and it was a pain to change them. I modified the inside of the battery box to accept a LiPo battery (https://www.amazon.com/TATTU-11-1V-450mAh-Battery-Multirotor/dp/B072PPRPRN). The end of the second video I posted has a picture of the components I used. In order to recharge it, I still have to remove one of the two sliding plates on the battery box to connect the charge cable of the battery to the charger. But the one on the top is not hard to remove.