Milković's inertial propulsion cart + some improvements.

[Merg]

What I have seen in this video was the fact that the SAME metal ball caused the cart traveled 3 times longer path in the case when it acted as a pendulum bob unlike the case when it was simple rolling down and crashed at the cart's edge.
So we are talking here about the same metal ball and the same potential energy, but the work done (the distance the cart traveled) is different - greater in the case of the pendulum.
It looks simple, we don't need the complicated explanation for this.

[Cloxxki]

Well, unless an ideal situation energy transfer is sought for the bumping ball, the experiment is hardly very conclusive.

Perhaps the cart should be rolling uphill? If the pendulum is so incredibly OU... A cart that is wide for stability yet lighter than the weight of the ball itself (at least seeking preferable ratio) should be ridden UP a slope, the COG of the cart reaching a higher position than it started at.
A one-way clutch on the wheels could be considered (very common on rollerskis). The initial roll-back in both setup would be resisted, likely resulting is a greater and more reliably comparable cart travel distances. I case of an uphill slope, the pendulum would have the change to work its way up the hill, not slipping back donw in "dead" or counter-active swings.
For the sake of an OU device, features such as one-way clutches IMO are very acceptable. Like ropes are allowed for rock climbing. You're still to bring the work of mass * height.

[Montec]

I remember an inertial drive claim that involved a solenoid and spring. At the correct operating frequency the wheeled cart would move across the table but it all boiled down to the difference between static and dynamic friction in the wheel bearings. Can friction also be at the root of this inertial drive claim?