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I did come up with a solution but I am absolutely horrendous with cad. In a nutshell extend 2 thin pins from the front section, which go right through the entire object and attach to the turning part on the back. Slits through the object would only need to be a quarter of the rotation.
Using this idea, you could also make the back turning bit a lot smaller.

In a nut shell, cut 1/4 rotation slits through the whole object, and user turns the front section by hand, which attaches to the turning section you are currently using via rods. Damn this is actually a lot easier to think about than it is too explain lol. I wish I could cad.