Maybe the first 20secs of that previous video is part of where Sjack Abeling got his inspiration.

Maybe he got the leaping into the air idea from the first 20 seconds of the previous link.

I've been out of the game, hadn't seen that Abeling website. He's giving pretty big hints, I now realize.

Says the upward side is "light". Makes me suspect the weight join it with excess speed versus the place on the wheel where they join. With curved slots as we've seen of him in the past, the weights, given some good horizontal speed at the bottom, could be radially catching up to the upward side of the wheel.
The "jumping" longitudinally, doesn't need to be a real jump. The Dutch language kind of implies it, but I'd also also accept the weight moving off the wheels at the upward side, around main axle height or higher, and shifting to a near horizontal support ramp that's OFF the wheel. The weight could then be dropped to hit the wheel with some speed, radially catching up and tranferring some impulse, but still keeping momentum on or off the wheel at the bottom, to hit the tighter bend upward, transfer some energy to the wheel before locking onto it, and being lifted quite straight up near the main axle.

Random thought.
Imagine the weight indeed freefalls (clockwise wheel) from say 2 to 4, and then lands on a pring loaded lever that tightens the weight's inward trajectory and leaves it would do good residual speed for the hard work on the early ascend. The moment the weight leaves that lever, there is a snap back that would positively drive the wheel late in that phase, for the weight, when the weight really at that moment has some decent radial speed, going largely horizontally at the rim of the wheel and perhaps even faster than (being off) the rim.

The weight may have a pretty elaborate path around the wheel, and may even at not one moment be on a circular trajectory around the main axle. Shifting between freefall, helping push the wheel down around 2-4, then pushing again from 6 to 7 or even 7 to 8, and then a passive phase where the momentum of the main wheel is lifting the weight, but hardly necessarily in an orbit of the main axle, At 10 or even 9, it could roll through a trap, transition to a near horizontal path and get freefall from 4 or 3 again.
Perhaps the free fall could be from the height of 12, but above 3 and then do the mother of all freefalls to 3, transfer a lot of momentum there, fall through a trap again and then ROLL across the rim, faster than the rim itself, arriving at 6 early and then doing a vertical push against the wheel. If falling from 12 height, the work up would be going higher. With so little time on the wheel, let along a fixed location on the wheel, it may hardly matter whether you drop from 3 or 12. 12 would just be higher energy.

Anyone here proficient with these simulation softwares I used to see on forums?

Intuitively, I sense there might be something with the relationshipo between the freefall energy (not height or speed), work down on landing, kinetic energy achieve at 6 (could be below 6, I don't know whether that would help, simulation might tell us), the work done on the way up, and how much the wheel needs to work to get the weight to the freefall height. Where the weight surfaces at it summit, left or right, doesn't matter at all. Abeling says that it "jumps", so I suspect it summits left of the axle, tranfers to the right while off the wheel, and then only rejoins the wheel (momentarily or partially by transfering energy but never slowing down to wheel speed and radius), to leave an upward left strike. In my theory, the lifting is the hard part, but the wheels has its own momentum and gets help from eight weight once or twice.

The much discussed tightening radius from 6 to 8-9 MIGHT be the holy grail where the centrifugal force is able to bring anomalous work. A smart exact curve to be taken to make it all work? Don't tell me it's the gold ratio curve...

I like the idea of the weight exceeding wheel speed at 6, making the tight bend, and ending up pushing the wheel as it transition to the radial that was at 7 or 8 already when the weight just passed the 6 position and actually doing some work to the wheel on the way up.
Abeling mentions the wheel being light on the upward side, that might indeed be the vertical car jump thing. That car goes nearly all the way up, and doesn't do work on the way up.

Abeling mentions a stationary moment for the weight from which it's accelerated. Now that could be a previously loaded spring that lifts the wheel to its summit. If that spring is mounted to the downward side it's a double kicker, but harder to accomplish. The spring load could be a sub system loaded when the weight lands (catch is mentioned), and it could be timed to not need any spring at all, just a well placed off-the-wheel lever that is hit by a falling weight and then kick another to its summit.