I knew it! My ceiling lamp is Art Déco, not 1950s. I. KNEW. IT.
Proof: a lamp recently come up for auction at Bukowskis Market. The image links to the auction.
The same style, the same wrapped shaft with fringe, the very same shape to the arms, same veneer. There is even something under that fringe that's pushed too far down. The differences are: three arms vs. four, shape of the cups, and the shades. But still, they are so incredibly similar, that I'm totally confident in declaring my lamp Art Déco as well.
I mean, look at it! The fringe and the veneer would have been very old fashioned in the 50s. It's not impossible, of course, that I'm wrong, but it "read" Art Déco to me even before I saw the other lamp. I am very happy that I did bid on it, even though I wasn't totally serious about it at first.
The friend who helped me with drilling on Saturday, relocated this lamp from the kitchen to its rightful place in the room. I love it there. It's just the right amount of hang, and spread of the arms for my room. With the lamp there, the room has now reached the limit to the wood textures, one more and it will be too much. The ceiling cup is still not fixed, but that can wait, the lamp works (in more sense than one). It's where it belongs now. And it's Déco! I knew it!