After a much experimentation, much of it making overly complicated mechanisms, I finally went back to basics and tried using a normal regular servo to move the bellows. I'm not sure why i didn't try it first but I think it was because of difficulties in getting the "arm" to raise - nothing I tried had enough torque until I found a geared stepper.
Anyway, here's the video of my test run:
The code is super basic, just using the standard Arduino Servo library to control the motion. I want to smooth out the motion if I can. If possible, I hope to find a servo library that allows steps less than 1 degree (or, if I have to, write my own).