The test boards came back today. It turns out that the Torex chip and the latest TI contender (the TPS61097A) are pin compatible, and I just misread the Torex datasheet. So one of the boards was a waste, but the other was able to test both.
The TPS61097A wasn't a lot better than any of the other TI hysteretic chips, but the Torex was. It wasn't as good as the NCP, but it will do. With the bench supply (1.8v) running the calibrate sketch, it draws around 40-45 µA so far as I can tell. When you look at the current on the scope, what you see are big spikes spaced around 4 ms apart, with mostly noise between them. The output voltage has about 20 mV of sawtooth in it that has a period consistent with that. For this application, that much ripple is acceptable, as long as it's consistent.
The price is a little higher than the NCP, but not critically. What worries me is that while DigiKey and Mouser both stock the part, their supply looks rather constrained to me.