Yep it screams “4th axis”, but that is not going to be easy (this solution might only take a few weeks)
I would probably try and go with your “slices” approach instead:
- import your 3D model (the one you printed) in e.g. Fusion360 or some other CAD tool supporting slicing.
- use the Slicer plug-in, adjust the slice thickness to match exactly the thickness of those maze walls, and the number of slices such that the transitions between horizontal slices happen right at the heights where horizontal walls start/end. It might take some trial and error, and it might require to adjust the 3D model, it’s hard to tell from the picture whether the “corridors” are an integer number of times the wall thickness in width/height. Do I make any sense ?
- you would end up with something like 32 slices, judging by the pic.
- cut each individual piece on the shapeko
- stack/align/glue them. You may need to make a centering jig
- sand the outer cylinder surface and do finishing (in your case painting the thing black + painting the outer surface in gold.
Not a piece of cake, but doable and it would achieve the correct geometry without the need for a 4th axis. It would also allow to get creative, e.g. alternate slices of contrasting woods, to give it a funky look.
Happy to help (with e.g. the Fusion360 slicer) should you decide to use this approach!
EDIT: as an example, on this random Thingiverse example:
Slicer does this:
and produces thirty-two 2D slices like those:
than you can then import in CC to create profile cut (you will probably need to use a small endmill, to keep the inside corners relatively sharp)