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··schizophrenic pizza orderer and watch collectorThe crown puzzles me.
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No, I think you should leave it up. It just seems different that other similar watches I have seen. That doesn't make it incorrect or a frankenwatch, just different.
The printing on both dials are also slightly different. That is common and I think they are both original dials. Once you get to the mid 1960's, Longines dial finishes began to become synthetic lacquer, which make for a more durable finish. So dials from this period are generally in better condition than other watches only a few years older.
I have some concerns about the "Stainless Steel" engraving being rather shallow. That would indicate some sort of polish and re-creation of the original finish. This is done all the time in restoration work, but if it were, I would not call such a watch New Old Stock ("NOS").
I think the point of this examination on my part and others, is that true NOS watches are extremely difficult to find "in the wild" as you say. The hang tag looks correct for this model, but have you had a watchmaker verify that the serial number and case reference match the tag? I just have questions as to whether it is truly a NOS watch, or just a nice specimen that has been expertly restored, but is not NOS.
Hope this helps,
gatorcpa