Just to give a progress update on this, I now have a complete Perfect/Final Edition .neo file running on NeoSD carts. This new .neo that I built today has all of the data from Perfect/Final Edition, not just the P1 ROM that I posted earlier. It is the full, original ROM that Yuki originally developed and used at the location test. The new story mode works in Japanese but doesn't in English. Why? Because the Samurai Shodown Collection is doing some real time edits to the Final Edition ROM to make the story mode work in English. Yuki never originally made the story mode work fully in US/Euro mode. Same with the logo for the game when running in the SS Collection. It's being appended into the game in real time. That's why the original ROM data for Perfect/Final Edition is different than what actually runs in the SS Collection.
Anyways, I guess you could say mission complete. The original Samurai Spirits Zero Special Final Edition is now fully dumped and running on real hardware! Again, here are pictures of the new .neo that I compiled today, the full Final Edition ROM. Note the new background on the start screen thanks to the Final Edition C ROMs.