Anyone have any experience with action cameras...along the lines of the GoPro type? I'm looking for a camera for recording timelapse videos of my drawings. I have a Nikon but unfortunately there's a time limit on its video function. I guess I'm wondering if there would be a lot of perspective distortion with those sports-type cameras when recording a tabletop/artwork

Perspective distortion is a function of shooting distance. Geometric distortion due to lens design is the issue with most wide angle lenses on such cameras.