[apalrd]

You can use JVN's mechanical design calculator (posted earlier) to solve this.

Use the Linear Mechanism sheet. Set motor specs, drum diameter, etc. as appropriate and set load to 1/4 of the bungee force (since you have 4:1 mechanical advantage). Set Travel Distance to the length of pull in, which you can figure out from your design.

We used a gearbox design similar to that which you speak of (pulling the gears apart) in 2010 on our kicker. We used a window motor which did not backdrive (which will not be nearly enough power this year), and opened the gearbox to kick. We only engaged the gearbox again after the kicker hit the hard stop and was not moving. We needed quite a large piston to keep it together. We ha no reliability issues with the gearbox at all, but we did kill 1 window motor. If I were to do it again I would probably put a ratchet somewhere in the high speed end of the gearing, on the motor side of the opening gearbox, and use a larger motor (probably a miniCIM or CIM for this kind of load and pull in time).