Ok, here's the latest development in this saga of this cabinet:
A friend told me about a local locksmith who was exclusively mobile and I called him. His prices were reasonable so I went for it...he had a key made in about 15 minutes, using a barrel blank I already had. He just cut it a little. He told me to keep looking in shops for old keys of the same size, and he could stop by and cut more. Apparently ordering a blank in this size would be about $20, so this will give me an excuse to prowl some antique places.
NOW, when the upper cabinet was opened, I discovered a medallion fixed to the back wall on the right, which would have been above the phonograph player. It says "Cheney Talking Machine Company". I looked them up and, as near as I can tell, someone had this cabinet modified not only for the "talking machine" but the left side has some added wood that's clearly for organizing/storing vinyl records. That bit is not all there but it's definitely made with a machine, and has screws in it. (Even the locks don't have screws, nor do the hinges).
My working theory is that someone wanted a phonograph player (the new very expensive one...it cost $240 in 1914) but didn't like the look of the cabinets, so they had one built into this cabinet, which is much bigger and more ornate than the cabinets made for the machines. The company was in Chicago but I suppose someone could have built it into the cabinet elsewhere...still, the fact that they'd go to the trouble of mounting that medallion makes me think it might have been done by the factory.
I'm adding new photos, and giving a shout out to Travis, who made my new key. :-)
If anyone knows anything about this new twist in the story, I'm all ears. Thanks!