There supposedly was a modified "Dancing Dolls" produced by Gottlieb (according to the ipdb). It was an experimental add-a-ball machine.
Oddly, your machine has starburst bumper caps on it which came out much later.
I've seen some woodrail games dropped into metal rail cabinets before, but if this is the real deal, you might have something there.

I believe the material you are quoting refers to "Flipper", and not "Dancing Dolls". "Flipper" was the first wedgehead, first production add-a-ball game, and the first Gottlieb metal rail game. I've seen several in their original woodrail cabinets, and the cabinet artwork is similar to "Square Head" as is stated in the article you're quoting.

It could also be that your lower cabinet is actually a woodrail cabinet that had an aftermarket metal rail kit installed. The way the woodrailed lightbox is installed suggests that the lower box is a modified woodrail cabinet.
I've seen these metal rails tacked onto some of the later woodrail titles. It was likely done by operators in an effort to "modernize" their older stock once the metal rails games started appearing.
The cabinet paint and serial number don't appear to be factory original, but obviously were done long ago.

Nonetheless, a great find. I wish I were closer. BTW, "Dancing Dolls" was the last Gottlieb game to use lamp display scoring. All EMs to follow used score reels.

Probably another attempt to modernize the look of the game. This suggests that the game may have been operated into the mid sixties or later.

When did Gottlieb stop stamping the game title initials after the serial number? My '57 "Royal Flush" still had "RF" stamped at the end of it's serial number.

$600 for all? What else did you get?