Success! Oh Happy Day!! The flat original animated GIF layers, after being Grouped and Duplicated into the 3D Book template .psd, managed to hold their alignment as a group while the scale, rotate, and skew tranforms were applied.
After that, it was necessary to create 42 frames to re-make the animation (copying GIF layers to another file as a group keeps them together and in order as layers, but the frame animation information is lost) and then sequentially re-assign the GIF layers to the frames in order and then re-apply the frame intervals to restore the animation.
But it worked! Just as it should. No photoshop futzing required.
Hooray for the tool allowing the implementation of a vision in support of the refinement of a technical skill and acquisition of new learning all while some Art is being made.