Nicely written article Nico!
The hands on your watch do have lume, check the hand's tips carefull.
A 1961 German pricelist at least refers to the DSA.
I don't buy the story the american brench had the idea of creating the DSA, more or less I'm convinced JLC just "brainstormed" about the additional use of the alarm disk. The usage is similar to Parking and Worldtime.
For a "die hard" collector only in-house movement powered JLC's are true JLC's, so the chronograph stuff is out of the limits and actually mass production since the entire watch came from a 3rd party and was used by plenty of other watch companies.
The american model with day/date feature is for sure powered by an AS movement (like most of the "Club" watches) and in my eyes questionable because the case seams to be identical to the Deep Sea Master Mariner and was available as spare part some years ago. (I still have an NOS case left). Same with the funky dial which is still available when you dig deep enough.
Unless I see an unaltered catalog entry or an advertising I don`t believe this to be real. I just have seen 2 examples so far, one offered on ebay the other you show coming from JLC's marketing department.
Cheers - Ilja