The brown horizontal line represents the rail supporting the axle. Below it is a reasonable guess of the position at release with a verticle line joining the center of mass in the two diagrams. The center of mass will fall straight down so the counterweight will have little lateral motion and be almost directly below the axle at the stall. That is the desired point of release, and it should release at about 45 degrees. I d expect a longer sling to be optimal.
Longer slings mean that the ammo is released higher.
Since Ron Toms new machine only constrains the horizontal motion of the counterweight, it should behave very close to this model. His constrain might be the easiest way to keep the whole thing from running off the track.