Hi Colin,
First I think it’s important to understand that all of Joseph Pilates' work was not recorded in his book, pictures or visual recordings. We are teaching a living tradition passed down from generation to generation. It would be nice if everything was documented for posterity but it's not. What a dream that would be! Even if it was though, it would be a snap shot in time and I can’t imagine Joseph Pilates desiring that we only teach was documented.
However, I do appreciate your desire to know the roots of what you’re teaching, that’s important to me too. I was taught the Mermaid by Romana as is in our manual (she called it something different then) and other variations of it, too. She taught me one where you slide out and in on the floor. One arm slides out and then it drags in pulling the body up to the starting position. It’s truly like a Mermaid.
Additionally, I was taught Mermaid by Kathy Grant and Ron Fletcher which are similar to what Romana did.
There is also Mermaid, as you know, on the Cadillac, chair and reformer with numerous variations. The fun continues with that exercise. I hope this satisfies your interest!