[DMetalKong]

Judging by the reduction, winch can be discounted from the possible ideas because you would get a ridiculously slow lift speed geared that low. That brings us to arm. At 1500:1 a FP motor can spin at about 60 deg/sec.

At 1/3 stall torque, a 14" arm supporting the weight of the robot would require approximately the reduction you described. Added to a lightweight apparatus raising the robot height to 60", this comes within grabbing distance of the bar. This would not bring the robot clear of the platform when raised, though. If, however, the robot is starting from the top of the bump, it could easily clear the platform when raised with only a 50" or so robot. This brings into question the raised center of gravity when navigating to the top of the bumps.

With a scissor jack, the linear speed of the motor would be multiplied by the number of links in the jack. Added to the fact that a lead screw would make a very convenient way to achieve the large reduction you want. Since the scissor lift also can achieve a large gain in height with a small retracted space, as well as the large reduction and issues with the other two designs, this is my guess for #2. As for #1, I am unsure of the math behind lead screw reductions, so I will leave that for someone else. ;-)