Dear @idyllosch - welcome to the forum.
your question spans a wide field.
As long as you want to work with 2d-sheet material / laser cutting - maybe first try to find a few references that still have the biomorphic look you are after.
Or are you already happy with a precise version of your cardboard mock-up?
the challenge here is, that - from a geometric point of view - the surface should be developable, and a standard screw-like / helix surface is not.
looking at your rhino file - do you really need 3d data ?
Maybe you can just do a few iterations to fine-tune the 2d shape that is cut by the laser ? so mainly work in 2d and have the 3d only in the real physical world ?
i think you need to narrow down your questions to a more rhino-specific question - otherwise people will point to This is not a do-my-work-for-me group
hope this helps - good luck with your project. - tom