I fixed the camera shift this morning, which created an odd tilt when moving sideways, but that's preferable to the previous behavior. I intend to try to tweak it some more, but I'd be comfortable releasing the game with this camera behavior, so I'm moving on for now. It has caused me to believe that the game will cause motion sickness, however.
Video:
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I've noticed before that I need to hide the mouse cursor. Sorry about that.