Kudos to you
Mr. Doppelgänger! REALLY Nice Video - and I found it very interesting!!!
By the way, after you video played - another one immediately came up after - and it's a cool one (purely music):
However, let me NOT Totally Digress from the topic at hand...
Now, I've been trying to hit your problem from a Different Angle - and I KNOW it's NOT the angle you seek. But, I would REALLY like to explore this angle with YOUR Assistance! That is - instead of painting the polys - instead - assign color/print head to Parts of an object.
As such, yesterday I created a Simple object, did proper boolean operations - so that the Object is made up of multiple parts. This is what it looks like in Prusa Slicer:

If I temporarily hide the main box - this is what the parts look like - as you can see the names of the parts in the slicer:
I attached to this posting reply the STL file - as well as the 3MF file I created using PS - where I properly split the object into it's component parts - and - ALL parts are in the proper positions.
Problem is - I do NOT have a toolchanger - and so my PS is NOT setup to allow me to paint the object by parts - and assign print heads. So, Mr. Doppelgänger - if you do that for me, and make material assignments - and then re-upload the 3MF file - I'd love to then take a look at the UnZipped contents of the 3MF file and do a bit of an analysis - to see how the slicer applies the tool head assignments to the parts. Cause - I'd love to figure a quick way to do your permutation assignments to the object.
Of course, you're probably going to tell me that someone on the Web has already done this. And, I would NOT be shocked - and then it would be a MOOT Point for me to continue in this particular direction...
-K