For a motor, I used an old craftsman 14.4v drill.  I've collected old cordless drills like this for projects where I need a powerful gear motor.  They are often tossed out because by the time the batteries fail, replacements are difficult to find, or as expensive as buying a whole new drill.  Further, the chuck makes it really easy to couple the output into projects.

This model has a fixed gear box, with stated 0-600rpm.  I did some bench testing to figure out what I would need for a power supply.  One of the catches with these types of drills is that the batteries themselves are the current limit, so they can draw a lot of current from a DC supply, especially when stalled.

In testing, I found that powered by 5v instead, the speed was reasonable, drawing 2-3A with no load, and 6-7 when stalled. The torque is much lower, not even enough to engage the lowest clutch setting, but it seemed plenty powerful to lift the screen. With 12v, these current numbers were higher.  I could run from 12v, and use the integrated speed controller, or if from 5v, I could remove it.  

I dug through my salvaged power supplies, initially looking for a 12v one, but also found a 5v 100w cage supply, and decided to go with that as it would make a smaller case.  In the end I tweaked the output voltage up to almost 6v for a little more speed. 

This resulted in a 5 second lowering time, and 6 second rise time, with a single fabric backdrop.  I expect it'll slow a bit further when I add a second or third due to the increased load.

To mount the motor, I simply drilled a couple holes through the plastic handle after the speed controller was removed and screwed it into the mounting board.