Thanks for sharing your immense knowledge with us. Should not be a problem to share an old C24 or Ebay pic here...
I hope you're right... Well, let's try ! I already made a private mail to DirtyDozen12 with the info so I'll try to expose this in a better way maybe.
So first here's the 12.68Z chronometer I spotted :

There's at least two hints that drives me to believe it's genuine and was actually tested by the Bureaux Officiels. First, the movement's finish is unlike anything I've seen on other variations of this calibre. As I said, almost impossible to fake this, this movement is certainly one of the rarest 12.68Z variations. For comparison, I've included the only others 12.68Z with a Breguet overcoil I know of (well almost, but there's no need to include the stop second/chronograph versions for obvious reasons). From left to right, you have a 1930s Baume, an observatory chronometer and a british military WWW both from the mid 1940s. The Baume has the same finish as a 1930s 27.0 caliber but with the 12.68Z typical bridge layout. On the other hand, the observatory chronometer has the same bridge layout than the 27.0 (but was still curiously marked as a 12.68Z) but with a much better finish (Guillaume split balance, counter pivots on the escapement wheel and beveled anchor - only later 27.0(S) movements from the 1950s had a beveled anchor). Lastly, the WWW has the most basic finish of all, with only 15 jewels and no beveled steel parts (not even the regulator), but it's the only one to feature a shock absorber.

The 12.68Z B.O. chronometer (to differentiate it from the observatory's version) is clearly a unique variation : it has nickel plating with geneva stripes and a curious combination of higher and simpler finish, but in a such coherent way it can't be a franken (for example, the ratchet is highly polished and bevelled like on a 27.0 or early 12.68Z, but the winding wheels are still the plain ones found on classic later 12.68Z, or the hairspring stud is not beautifully screwed like a 27.0 of the same era, but the regulator still keeps the same high finish). Here's another chronometer to compare the finish, but because this one is in a gold case, as it was pretty usual with Longines then, it's not a 12.68Z but a 27.0 :

You will note this 27.0 has, like its balance wheel, a beryllium bronze anchor, a common feature of fine 1940s to early 1950s Longines. The 12.68Z BO chronometer pics I have here are not good enough to see if it has it too, but I clearly remember the other 12.68Z BO I have seen long before having this particular feature.
Now for my second hint, it comes from the serial number. From what I can read, the 27.0 and 12.68Z BO seen here are... consecutive ! It seems they were made just one after the other ! (Believe me, this really is pure luck, I spotted those watches in different times on different sellers - the 27.0 was sold on Time Titans - and actually only noted this today while writing this post...). Moreover, they point to 1950, a year which Longines submitted to certification much more wristwatches than usual (exactly 66 wristwatches submitted to the B.O. of St Imier if you exclude automatic movements, previous year only 6 were submitted and following year only 5).
If you put all this together, I think the two chronometers presented here are extremely likely to be genuine, don't you think ?