You'd need a lot more space between them for that to be effective and it would not work for anything that moves because the images are also spread out in time.
That's why old school stereo cameras had their lenses much further apart and that's why they fired synchronously.
Would have to be a high FPS camera. Some cheap linear rails and a NEMA 17 motor. Of course you would have to get the "sync pulse" out of the camera, then you would probably have to do a delay move to move into position before the next snap.
Sliding it back-and-forth would create too large accelerating/braking forces. Easier approach would be to put camera on a rim of continuously rotating wheel and take shots when it reaches positions of 90° and 270°.