The mystery is over. After all, R2-D2 wasn't the astromech calculating the warp trajectories for the Enterprise. Here you have the exact location of the cameo—and the capture showing it:
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]