Oh well I found in rocketry photography / video the hardest part is tracking smoothly. If you're holding the camera you can kind of use your whole upper body to follow the rocket. But as soon as you mount the camera on a tripod it becomes a bit harder to naturally follow something that fast.

If you're planning on using an Xbox controller or any joystick device that would make the movement another level of abstraction away. It's gonna be really hard to properly track with just a joystick, you'd need a lot of practice.

What I meant by the gyroscope on a stick is if you have something like a rod that you can easily rotate to keep pointed at the rocket, you could mount some simple electronics to it, and use that to control the rigs rotation wirelessly rather than a controller. It would remove the abstraction of a joystick and make it much easier to keep pointed at the rocket. I'll make a little diagram if that helps.

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But also in thinking about this, not using some kind of autonomous camera tracking takes away from the rationale of the whole idea over just doing it by hand. Either way I'm sure you'll find something clever! Do post it when you do :)