Wellll, turns out by save-to-USB problem may be simpler, and not due to the Hantek after all:
The only devices I have that the 'scope recognizes are a couple SD cards, 32GB & 8GB in a card reader.
Problem is that they're both read-only, even though the write-protect switch isn't in the locked position.
Looking online I learned of a problem with these cards I didn't know about: they tend to go read-only as the memory cells degrade. I think that's what happened with both of them.
(But oddly enough they both work in my camera, a Fuji X100 which has no trouble saving pictures to them.)
Plus the partitions are maybe too big for the 'scope (I think it doesn't like anything >4GB).
So I'll buy a new USB device, maybe a small thumb drive and try it (use a partition manager to create a small-enough partition).
It'd be nice if the 'scope told you it couldn't write to the device, but I guess that's asking a lot these days.