After using the kneeling chair more, I got reminded of why I switched away. The first problem I ran into was that it made using the mouse tougher on the right shoulder. This one might not have been entirely the fault of the kneeling chair; it was fixed by making sure my mouse was closer to the center of the desk.
The second (and more real) problem I ran into was that kneeling is much harder on the knees. I followed my own advice and tried to keep getting on / off the chair at a minimum. That helped, but wasn’t enough. My knees felt out-of-place on any days I would use the chair. Sitting cross-legged would also feel off; there was no pain, but the bones would make alarming cracking noises.
Anyway, I’m in a bit of a rut because the kneeling chair really does help my shoulders. Weirdly enough, the knee problem was not an issue during the months when I used just the kneeling chair and nothing else. To be safe, I’ll go back to using the computer chair as my main; whenever my shoulders feel extra weak, I’ll let myself kneel.