As noted in the update-to-yesterday, it looks like there's an interim solution to the ferschlugginer USB problem that's been plaguing me for the past week-and-a-bit.
While using a TI AM3352 processor as a USB host doesn't work right for a large number of peripheral devices, nor for some particular devices all by themselves, the Allwinner A20 seems to be getting the job done. And, now that the job is getting done, it turns out to be a good thing that the A20 is a dual-core critter, as the USB protocol stack is eating quite a large percentage of the available cycles.
I've got a cute little A10-based board on order (cheap); if that turns out to work (I'm guessing its CPU will be overworked, but I ordered it before running the test at full load), it's a Solution. If it works except for the CPU being overloaded, well, there's a slightly pricey A20 version of it available.
And there may (details are fuzzy) even be a fully industrial spec version available. And the board is open-source hardware, so a customized version is an option.
This got me looking at what Allwinner is up to. They also have a thing called an H8 (not to be confused with the Hitachi H8 family), which is an 8-core beastie, with the necessary Ethernet and USB features (plus a bunch of stuff I don't need, like video). Someone's using it on a cheap little board. Maybe the Far Eastern assembly houses have a supply? As far as I can tell, though, it's a commercial-temperature item, and I can seldom get away with such things. Wonder if it's available in I-temp at all.
(Yeah, I tend to insist on industrial-temperature components for just about everything, when I'm not demanding automotive- or even military-temperature parts. The application at hand actually needs to be I-temp when it goes to production, because it could be deployed anywhere from Anchorage to Death Valley, not to mention Foreign Parts.)
So, anyway. Immediate problem solved. Long-term solution in sight, and apparently not too expensive. Also, there are some awesome little chips out there.