Found it! The little ottoman.

There was a little voice in my head that told me I should return to a store that I SWORE I would never walk in again. It was, to put it mildly, a junk heap, barely arranged in vignettes of mostly kitschy stuff in poor condition and with goofy-high prices. 

But there was that voice. It reminded me of the corners literally piled with partially assembled, mostly damaged, midcentury stuff that could've been something if someone, anyone, had an attention span of more than 5 minutes. And that was exactly what I was looking for.

In one of those corners is exactly where I found it. Behind a screen and a surfboard. On top of a pile of who-knows-what. 

It has a problem that the little chair didn't have: missing hardware replaced with some that doesn't work. The wood may be a different color, or it may have been stained an ugly late-70s tone that we all want to forget. The weave of the cord is different, but quite nice. And it has a label-- made in Yugoslavia. All in all it looks like it will be a good match for the little chair.