I had sent a support request in for this issue, and got a couple of emails from 'John' at the helpdesk email addy. It sort of appears that my replies from gmail aren't getting back to him, though, so I'll post here, where other folks might find it useful too.
So here's the rub. Initially, the 3DxWare daemon would complain about a missing libXm.so.3 when trying to start it. This was resolved by installing OpenMotif - which, it should be noted, doesn't always play well with other Debian packages (I don't recall which, I'll have to check again). Anyway, 3dxsrv is happier, but finds no 'spaceball' device in /dev. The SpaceTraveler does show up with lsusb, and it does appear in /proc/bus/input/devices:
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I: Bus=0003 Vendor=046d Product=c623 Version=0311
N: Name="3Dconnexion SpaceTraveler USB"
P: Phys=usb-0000:00:1d.1-2/input0
S: Sysfs=/class/input/input5
H: Handlers=event5
B: EV=7
B: KEY=ff 0 0 0 0 0 0 0 0
B: REL=3f