Thanks for all the suggestions.
I thought about a stepper, but I really want a system that knows where it is when it wakes up! An un-geared stepper would likely not have enough torque. I also want a faster slew rate than a stepper would likely support.
The way that the roller inductor is made, there is no way to couple a linear pot to it.
I found that 20T pot on Ebay before John linked it. But at that price, I will go with 10T pot and a 2:1 gear train. I already own a 10K 10Turn 0.5% linearity precision pot. The links to the Robot stores were very helpful.