First off, I like how you posted this themed as more of a "guess what I am doing" lesson/game than a "Hey what is everyone else doing?" to provoke thought. It is a nice departure from the standard fare.
Can you please clarify if the FP motor is attached to the KOP FP gearbox, and then adding 1500:1, or is it 1500:1 directly from the FP. I am assuming you mean the latter since you were cocise on the rest of your comments.
Also, is your 5 second requirement only for the "lift" or also the deployment of your attachment mechanism
To throw out some FP Specs:
Stall torque: 0.45 Nm
Free speed: 15,500 RPM
Peak Power: 184 Watts @ 10.4VDC
I will throw my guess out that this is an arm based on the following:
1. You state "Drive sizing for an arm that lifts a 150ish pound robot", so I am guessing that might be literal
2. The FP motor has the highest speed to power ratio after the CIM. Since this works well into any of your three types, nothing definitive there.
3. Your requirement of five seconds would seem difficult to achieve with an FP 1500:1 with a winch from a speed perspective. A scissor lift seems possible, but only if it is already deployed, or if it is not required to hange from the horizontal bar, but instead from a side pole. From my experience controlling scissor lifts from
JLG, the weight to lift speed ratio is surprisingly slow if you want it to be done in a controlled (ie. safe) way.