Thanks for the new diagrams, allmee. I think I now understand how the no. 5 device is supposed to work.
The basic problem here is that this is a "bootstrap" device; it pulls against itself. All the forces are actually in balance. It will not move.
An analogous device, which I can describe here without violating allmee's NDA, would be as follows: a weight is hung from a string wrapped around a spool. Assume the weight of the spool and string is negligible compared to the hanging weight. The spool will turn as the weight pulls on the string. The spool is also attached to a mechanism that raises the spool the same distance as the amount of string unwound from the spool. (This can be achieved by putting gears on the ends of the spool that mesh with a vertical rack.) So the weight stays at the same height the whole time. When the string is all unwound, a platform is placed under the weight to continue to hold it in place as the spool is allowed to descend the rack and wind the string up again, which takes no energy. Repeat. (If you're worried about lifting the weight of the spool being a factor, just add a pulley between the weight and the spool, and make the spool's travel horizontal instead.)
Actually, of course, the torque on the spool from the hanging weight will balance the opposite torque on the spool from the spool-raising mechanism, and the spool won't turn.
Allmee, examine the torques on your worm gear carefully. Make sure to include the torque on your main pivot from the tension of the spring, which is transmitted to the worm gear through the shaft from the miter gears. I think you'll find that they're balanced.
Respectfully,
Myriad