I attached a long wire to the motor contacts and ran it over to my desk.  To control the motor I didn't need anything fancy, just the supply, power switch and reversing switch.  I could have used the original speed controler here if I wanted speed control, but I was trying to keep this simple.  An RC hobby brushed motor controller and servo tester could also have been used, and would have been much easier to install than the original one because it uses an actual potentiometer, while the original does not.

I found a case in my scavenged stock, in this case it was for a quite external 5-1/2" floppy drive.  It fit both the cage supply, already had an IEC C-14 socket and switch, and has a nice slim profile to fit on my desk under a monitor.  

A couple mounting screws for the supply, and a couple for a terminal block was all it needed.  I was able to reuse an existing hole for the switch.

For a switch, I was fortunate to find the less common, but perfect toggle.  It is a DPDT, with momentary on - off - momentary on movement.  This means that by default it sits in the middle, with all contacts open.  You can push it up or down, but a spring pushes it back to the middle when released.  As a DPDT, I simply wired it as a reversing switch and that's all I needed.  Normally the motor is off, but when I hold it up, the backdrop goes up, when I hold down, it goes down, and when I release it stops.

The built in power switch I left as switching the AC so the supply doesn't waste electricity when not in use.

The power cord ends up on the same side as the switches, which isn't ideal, but it wasn't worth making an extra bracket to mount the switches on the other end.  Regardless, it's tucked away and the cord isn't in the way.