Just some of my initial thoughts, nothing more....
I would have envisioned attaching the camera bracket directly to the servo horn. You'll want a servo with dual bearings, a steel gear train, and probably a disk horn for a more stable, larger contact surface.
You also may find it easier on the mechanics if the rotational axis was placed on the camera/bracket's center of mass axis rather than on the lens axis. The viewer will not see a difference unless focused on objects within a few cm.
Also, you should place the gyro as close to the axis as possible. Keep the twisted leads as short as possible for less chance of signal interference. Surprisingly, cameras can make A LOT of RF noise.
Make it as simple and compact as humanly possible I'd say, even if it requires a slightly larger, more robust servo.
You may be pleasantly surprised about the ease of use of thermoforming plastics such as Kydex and others. They can allow you to create professional-looking, relatively complex, light-weight moldings from simple wood forms in a short period of time using normal hand tools. Or even epoxy-fiberglass laminates work well and are easy to fabricate over home-made forms.
Steve, what controllers have you been using in your projects?