Still less 10 of these AA4 are known to exist
No the case is not like mine, but it is a correct 300 serial range AA4 case. The dial is a correct serial 3000 range AA4 dial. The case and movement did not leave St. Imier together originally. There could be records of a replacement later. But, I have a different wrist chrono watch from 1910 era where the Archives show an upgrade was made but Longines put the same serial numbers on the new part.
3166 Dial. Note, 3166 is all matching.
3166 and 3223 share same movement number and logo positions on bridge. The movement is many years newer than the case.
Still less 10 of these AA4 are known to exist
Hello DD12, you do not have the knowledge of how these AA4 were marked. This is the correct way for all AA4 to be marked.
If you believe the case is original, then the current eBay price could be 1/10th the price of it's true value. Longines bought the parts for 561. Not even a complete watch for more than $5000. Bernard had to make some of the parts. 3223 is a complete watch that needs a hair spring, balance shaft, and overhaul.
It is always hard to value these very early watches so that sort of insight on 561 is helpful. I was watching the listing with the believe that it may be solid value if it remained under 5k.
I am not sure that it is wise to appraise the value of a watch, made by a given brand, based on the amount that said brand paid for it on the secondary market.
AA4 in any form are very rare since most were not planned to be produced. Longines also has no actual records of "AA4". They are recorded as 20A. There is no way to count AA4 production numbers from the archives. I believe Patrick Linder was first to publish the AA1-AA4 terminology. We must remember that many different calibers were available after production issues were resolved at the factory for the true keyless 20A.
Also, these AA4 were expensive to produce. Each movement part was hand tuned to fit. These movements were literally hand "finished" meaning the adjustments have to be made to the springs, bridges and plates, not just the jewels, balance, and regulators. AA4 movement parts are not interchangeable. These are non-standard sizes.