Thanks, Carl!
Your clear explanation of the tradeoffs of the different ways of wiring the motors is just what I was looking for on that. It sounds like bipolar series is within bounds for what I want in performance right now. I may change to parallel later if it looks like it'll give me some advantages in use.
It's possible that current was the cause of failure, but there are some things that made it seem unlikely when I was troubleshooting. The unit didn't generate any significant heat, for one thing. Also, when it initially shut down it would come back after a short while switched off. I disconnected the motors and switched it on--it would run at 48V for a short while, then shut down as I described. Of course, this was after the initial event, so it may already have been compromised.
Also, a current failure should keep it from being able to produce a high output voltage. It comes up to peak output (about 51V) when powered on, then cuts off. Which sounds like a regulation problem.
Still, without a schematic and a real knowledge of the circuit, I'm just using a dowsing rod.
I agree on the linear unregulated vs. switching supplies for this application. I was under the impression that, at worst, I was buying a linear regulated supply. Since it's in a can, I didn't see the insides to know the difference and the weight was light but things have come a long way since the days of boat anchor transformers so that didn't clue me, either. *shrug*
At any rate, I think the long term solution will be to replace this supply with an unregulated linear, as you recommend.
If I do hook up the 24V supply, I'll monitor current until I see what sort of a draw I'm getting, and hook up one motor at a time. That'll give me more information on what I'm doing, too.
Edit: I should probably also note that I've got the Gecko set up with motor current resistors, 2.2K on each of the three motors. I measured each one before installation and selected ones closest to 2.1K I could, so I at least know that there aren't any that aren't in the correct range. At any rate, this should mean that the Gecko is putting out a max of about 6.6A. Exactly how that relates to what it draws is something else, of course, which I'm still looking into.
Latest as of 5:45PDT 4/11: More data. John from Keling asked me to check the fuse. I popped the power supply open and pulled the fuse. Zero ohms. The fuse is still intact. Also, there's no sign of component damage inside otherwise.
More news: Probably just a bad power supply. John at Keling will refund my money on this one when I send it back. I'll be ordering another supply (from Keling, I expect

).