kaberett | preposterous puzzle: thoughts so far

The context is Simone Giertz's Incomplete White Puzzle, which A got me partly to troll me and partly because they thought I'd enjoy it and partly because getting the bundle of all three puzzles gets you 20% off individual list prices.

Current status: 105/"500" pieces in their final positions, plus another 57 no longer singletons. I have several semi-sorted categories including (in the halves of the box) "could plausibly have come from a reasonable puzzle" and "bullshit", and (on the table) Swoopy Bullshit, Offset Noses, Weirdly Straight, Multi-Nose Bullshit, and Featureless Curves.

Per the subject, thoughts so far, broadly They Have Done A Really Nice Job:

there are Distinct Classes Of Features, so that you can e.g. take all the pieces with Ridiculous Half Holes and sort them out relative to each other as a well-bounded subproject with a clear success point
once the edge is in place (with a whole lot of decoys left over -- but satisfyingly left over), there are a range of Very Different shapes you can use to get leverage...
... and a bunch of pieces in each relevant class that look plausible enough that you have to check, but not so plausible that you have to guess whether or not you're right (so far I have misplaced with any degree of confidence a single piece in the edge, in an off-by-two error, plus another distinct edge bit that was 50-50 on where it wanted to go while the edges were still in lots of horrid little separate runs)
the ABSOLUTE GENIUS of the one missing piece: even once you've been through everything (everything) twice, you still don't know whether you can't find The One Piece That Should (see above) Be Obvious because (i) you're just failing at observation, (ii) it's doing something sneaky and counter-intuitive, or (iii) it's the one that's missing (unless you go back to check the listing, but I am sort of hoping in my heart of hearts that there are 500 differently incomplete variants... or, well, ~400, if you reject any variant for which the missing piece would be an edge piece, As A Treet)

I am having a very pleasant and soothing time, and I am trying to break up the hyperfocus by instituting a rule of Get Up And Do One Unit Of Something Else After Every (Contiguous) Piece Placed, and yes that is me rules-lawyering after the fact...