Good News!
Today I received a Model M-122, old-style, with big side-button legs, hoping that the top case shell would fit an F-122. It did!
Furthermore, as soon as I touched it, I realized that it was made from the same plastic as the Model M cases (softer, tougher, more flexible) instead of the harder, more brittle Model F plastic. This was very good news, and what I had been hoping for.
The label was gone, but someone had hand-written "1386887" in pen where the label used to be. Presumably, this was the part number, but no way to know for sure.
The Model M bottom shell piece was full-size and plastic, rather than the metal pan and narrow attachment strip of the F. The case screws were a smaller diameter and went into all-plastic sockets rather than the embedded metal sleeves of the Model F sockets. However, the placement is the same, and the Model F metal pan and narrow attachment strip fit properly with only a bit of modification, using snips or a Dremel to shave down some plastic tabs, provided you use the M screws.
So, there is now another remedy to the chronic Model F case breakage, although those first generation Model M cases are not common, either.
Good luck with your journey!