Heyoo,
I know this was a couple months ago, but every once in a while I Google the 15705 because I have one and want to see what's going on in the market, etc.. I stumbled upon this post and just wanted to reply to let you know I have the same one as you. You seem to have an earlier Serial, as mine starts in 4_08. Not much information, as you already touched upon everything you've found. I bought mine at an auction (along with one that ended up being a fake), but same movement as yours with the 78X. My strap seems to have been replaced at some point, as I do not have the Cartier one, nor buckle on it.
Does yours have the blue hands, or is that the picture making them look black? Mine hits all of the same marks as yours. My crystal is a little beat, and I wonder if it's even possible to replace. Seems to run fine, I haven't done a test or had it serviced to see the condition of the movement. And I believe you are right about the Brass as the base of the metal.
I noticed you also found that Youtube Video of Wristwatch Revival that did an in-depth. Pretty cool watch, are you wearing it or just holding on to it? I want to find the right strap -- Green, Blue, or Grey Suede and make it pop. I originally thought I would just flip it but I dig it and it's a classic.
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