Thanks Andy for the pointer.
Ok, figured this out (sort of).
I disconnected all USB devices and then went into CONTROL PANEL -> Mouse Properties (Hardware) and noticed there was still a "HID-compliant mouse" device listed -- so I UNINSTALLED the device. Then, one at a time, I plugged in each of the USB devices (4xUltraSticks, 2xBlackhawks, 1xU-Trak, 1xLEDWiz, 1xiPac) ...
After that, all the devices re-connected on the machine, and life is good. Both Windows XP and Mame32 recognize the U-Trak.

David
(I tried with/without the extension cable and that didn't do anything -- so I did the disconnect trick above)