Yes, I'm sure mine is a 637. There are numerous photos of 637s out there that match mine like this one on the Radio Attic.
https://radioattic.com/item.htm?radio=1310025
I see hwat you mean about the power transformer though. Seems that the 637 'A' should be series strung. I can't say for certain if mine is the original back or maybe it's a factory screw up ?
Here's an original Emerson service manual depicting the various models on it's cover including the 614 and 637.
https://www.manualslib.com/manual/81...erson-614.html
I'm really curious to see what chassis is inside my 614 now!