The mystery is over. After all, R2-D2 wasn’t the astromech calculating the warp trajectories for the Enterprise. Here you have the exact timing of his stellar cameo—and the frame capture to prove it Updated
https://gizmodo.com/is-r2-d2-driving-the-enterprise-5261285
During the Drill Machine sequence as the Enterprise comes out of its barrel role amidst destruction of the other Federation ships above Vulcan, we cut to an interior Enterprise bridge over the shoulder of Kirk that is looking out through the front viewscreen. In space, R2-D2 is floating in the debris from about the top middle of the screen to the bottom right.
Poor R2. [Oh No They Didn’t]
Update: The scene is that but that is not R2-D2 according to one ILM Star Trek effects supervisor. Unfortunately, he and Paramount can’t show the scene yet.
