Now that he’s got it in a computer, it might be interesting to ask questions like: what’s the geometry that has the sharpest transition, while also preserving some sort of “good view” of the two subjects from a lot of viewing angles. I think this is not even a good phrasing of the problem yet, but phrasing the problem well is part of the fun.

I guess this could be interestingly image-dependent. In particular she’s quite pale, so I wonder how many surfaces could be shared between the two images.

That'd be pretty easy to throw into an optimizer. For each configuration, you could calculate the "fitness" by just sampling the anamorphic rendering at various angles and do pixel by pixel comparisons to ground truth rendered single-image portraits of the two images rendered at the same angle. Could use nearly any metaheuristic super easy with that setup.