To bring this little saga to a close, I built a little AC adapter for my Fuji Finepix digicam: brought in 5 volts from a little Samsung wall wart, put the regulator and an electrolytic cap in a film can on a little piece of perfboard, and brought the power out to a 2.5mm power mini jack.
The long and short of it is, the camera doesn't work on this supply. It puts out 3.25 volts alright, even when plugged into the camera, but the camera just sits there and does nothing. My suspicion is that the power jack is just not quite the right size to make contact (or else there's something screwed up inside the camera that makes it not accept external power, which seems unlikely).
So I'll probably bite the bullet and shell out a little $ to buy the AC adapter made for this camera (found one on the internets for about $12).
The camera itself (bought for $1 at Oakland's White Elephant sale) works like a charm; just got the USB cable for it today ($4.75).