Thanks to my great impulse control I bought a small, very cheap desktop CNC (TwoTrees 3018S) and verified the g-code in POM. Tomorrow I'll cut down my rod of PEEK and run it through that. The end goal is a thermal isolator, but mechanically rigid holder for my HPGe at 77 k-ish. At least in POM it's pretty damn rigid, and I'm qute happy with it!
And yes, linear rails and a new spindle for the mill are already ordered and shipped