Luckily I have never encountered this (nightmare) more than as an experiment of thought!
Do you have any info about what lens and focal length was used?
My first idea, depending on how good quality/resolution the photo is, and how bad distorion is. I would try maybe correcting it to linear with Photoshop, Lightroom, PTLens or something like that. And then match and render as usual and then, distort things back to fisheye in Photoshop. You might loose some pixels in the edges, and definitely loose quality this way. But it is one way… if all other fails.