For all of these watches, you should look at this exceptional website: https://www.calibre1040.com. Which is run by @Andy K . I have never seen a case like this, and it does not seem to be mentioned on the website above. However, it is a strange thing to fake.
Here is mine. Compared to the OP images the pushers look too short and the chronostop hand is the wrong colour . The case looks like it has been polished to within an inch of its life.
Not a terrible example, but requires a number of hard to find parts and the time and expense that goes with the finding. I would think about buying this at $1000 but pass at much more than that.