rhino is the right tool for this.
you can’t just offset the initial polysurface then expect all the intersections to arrive at a result of easily machinable miters… because what you’re expecting to see happen isn’t possible with the input geometry… you’ll have to figure out a system (maybe not the right word?) to make this possible…
once the logic(?) has been figured out, you then work outwards from there… adjoining planes will be positioned more strictly based on maths as opposed to just looking cool.
but without going down that road which would be required to get machinable / well fitting miters at all intersections, there are maybe some other methods you could try… with the tradeoff being more finicky assemble , or, require neat thinking on some sort of brackets etc.
using your model, two approaches might be:
something more node based… all of the panels are cut square (no miters)… gaps are left in between panels but this eliminates most or all of the complications involved with intersecting all of these surfaces… but increases complications with what to do at the corners of the triangles.
a sort of similar approach but without the gaps would be to overcut all of the miters… cut everything at 45º then the long points will meet tightly without the worry of collision from adjacent panels.
(view from underneath)
with the right brackets, the miters could probably be left as is… or you could fill them with a polyester resin etc…
from the top, (with a little luck ), the outer surface will look just like the model’s outer skin.
either of these two would be child’s play for a cnc machine to cut.
there’s another approach in which half of the necessary miters could be cut at a standard tool angle… say 20º… the other half of the miters would need to be cut according to the angles between the individual panels… numbers like 27º and 33.4º (ie- numbers which don’t have corresponding cnc bits)… it’s doable but you’d be better off with maybe a router and horizontal panel saw… track saw could do it too with enough patience… doing it like this would be much more work than having a cnc router cut the panels… the backsides of the miters wouldn’t match up perfectly (because one half will have longer miters than the other) but the entirety of the joint would match perfectly resulting in a strong glue joint…
this is the way you’d have to make the cuts with your current approach/shape and desire to be left with well seamed miter joints for glue & brads… it’s a lot more shop work (annoying shop work-- plotting points, a whole bunch of blade angle changes/tunings/etc) but not impossible by any means.