This is awesome, but the training schedule seems overly complicated. One would think it would be easier to have the balls initially positioned so that they fall into the feeding mechanism at the touch of a feather; probably at a place where food used to be served, so the cats are likely to be there and search for food. A cat should be able to figure out the procedure after knocking the balls in accidentally a few times. After this, it would just be a matter of moving the balls gradually further and further away from the feeding apparatus over time.
I've been busy and avoiding reading comments, but happened to see yours here.
Interestingly that's actually the approach I started with, using a cut slab of PVC pipe with screws for adjustable stopping points that initially positioned the balls at the edge of the bowl receptacle.
The problem was, at least with my cat, that he tended to nudge the ball in the wrong direction (despite my attempts to make my ramp one-way), and his first instinct to affect the ball was to use his paws, lifting the ball away or batting it out of the bowl.
Here's an example of how fragile and reflex-based I think these behaviors are (vs. levering some kind of affordance/object/goal-oriented intelligence), at least to start -- when Monkey was initially successful at carrying the ball into the bowl, all my training had involved approaching the feeder from the living room, to the feeder's right side. When I put the ball to the left of the feeder, he picked it up, approached the feeder, and about a foot away just dropped it and froze... apparently dumbfounded. It took more reinforcement and gradual variation with ball placement until he was able to generalize and approach the feeder from anywhere.