I created an account on BYOAC and posted in the Space Base thread asking for guidance from Le Chuck and his partners. Let's hope they see it and provide their help. http://forum.arcadecontrols.com/index.php/topic,140466.msg1581811.html#msg1581811
I looked around a little bit for resources for steppers with Raspberry Pi.
I found this hat (like an Arduino shield): https://www.adafruit.com/products/2348
Luckily, it can control two stepper motors by itself, and it has all the needed protection and stepper management circuitry built-in. There is also a Python library to simplify interacting with the steppers. According to the video, you can basically just tell it which direction to spin and at what speed. Sounds easy enough. It is designed to be stackable, so you can add another hat on top of it. That will be necessary for the errant ball solenoid. I don't know yet how to drive that. The steppers will require some external power, since the Raspberry Pi cannot provide enough on its own.
Tutorials for everything: how to assemble, wire it up, add external power, and program for it are available here: https://learn.adafruit.com/adafruit-dc-and-stepper-motor-hat-for-raspberry-pi
It's compatible with these steppers: https://www.adafruit.com/products/324
I'd have to assume these are strong enough to move our ICB bar, since these exact steppers are used in CNC machines like the X-Carve.
Adafruit also sells handy mounting brackets for these steppers.
https://www.adafruit.com/products/1297
One less piece to have to figure out how to fabricate, thanks to off-the-shelf components.