I, too, have some questions, but for the most part I'm fairly convinced that if the 9th hole was the number for the hole entering the Chambre, the 12th would have been the hole I've marked as such on the 2nd version of the map and photo. There are no other routings I can come up with leading up to the 12th hole that make sense, and no photo evidence I've seen that contradicts this theory.
As I said, I was thinking of something similar to your scheme, but had some issues. I don't think there is anything necessarily contradicting the theory, it is more just that we don't have enough information to adequately support it. I am still of the opinion that about all we can say with any degree of certainty is that the CBM "No. 12" hole in question was almost definitely not the "Chasm Hole," was probably located in the bottom of the Chambre d'Amour, and that it possibly utilized one of those big rolls or hogbacks visible in the photos.
Here are a few reasons why I am hesitant to get solidly behind this theory or any theory specifically identifying the location:
1. The photo supposedly of the 12th green. Looking at the background, then this photo ought to be looking from the green back toward the tee. Yet I don't see anything resembling a tee or a hogback between the tee and green. It could just be the angle or the poor quality, but I am not so sure that this photo supports the theory, except that it is reasonable that the green location could be about correct but it is really difficult to tell. Also, even if the location is correct it could be playing from the opposite direction. (When I first saw this photo my assumption was it was taken from the front of the green, which would be a more conventional way to photograph a green.)
2. I don't have a good sense of the dates of the various photos showing various man made features (greens and tees) or that the features were in existence at the time CBM was there. There were so many changes down there that I am not sure it is reasonable to assume that a feature we see in any of the photos was actually there in 1906. And there are features (greens and tees) in the photos on which you are relying that are not taken into account in the theory. For examples, in a few of the photos a green (or something) is visible across the road from where you have the 12th tee, and the location where you have the 12th tee was a green as well. And then there is the tee on the other side of the green where you have the 12th tee, and I think may have been the cliff hole tee. And some feature right in front of the house. Even the photo of the ladies teeing off (where they are dressed formally) shows part of a manmade bunker to there left of the teebox, suggesting another hole that we haven't really identified. In short, there seems to have been quite a lot going on in terms of different routings, and I wonder if we aren't picking and choosing a bit too much.
3. I've provided some descriptions for Golf Illustrated (which I will try to provide in full) but honestly I don't have a strong sense of confidence in any of the course descriptions from about 1895 to about 1908. The reason is I think about every description was written by Hutchinson, yet while Hutchinson was there in the winter of 1893-1894, he was apparently not there again until either 1908 or 1909 (I don't remember which one offhand.) And this alone makes me somewhat wary of relying on his descriptions of specific hole numbers. At some point around 1908 or 1909 the descriptions change from No. 9 playing down into the Chambre to No. 8 playing down into the Chambre, and I don't know if this was an actual change or whether the numbers were wrong on the previous descriptions. A shift in one hole makes a big difference when it comes to placing the No. 12 hole.
It'd be nice if we could narrow down the location of the Cliff tee, but I am not sure we can. In at least one of the photos it looks like they might be playing over a road, which would suggest the tee was over by what you have as the 11th green, but I cannot be certain.