Can I ask as a beginner stupid question? If that re-assembly is so important would not be easier to cut the material into desired thickness first then to assemble it together with double sided tape, turner it into a shape and take apart?
I'm just catching up with questions. I've made one duck puzzle, trying to make a second when the cutting of the segments went wrong. The bottom diameter is about 75mm. Anyway, about to trawl charity shops to find a suitable knife to convert into a thin parting tool.