I finally found time to get back to working on my laptop, whitestar, and:
Got the Prism54 mini-PCI wireless card working at last with wpa_supplicant;
Found out how to get the case all the way apart, gaining access to the second memory slot buried under the touchpad;
Successfully modified and installed the 802.11g antenna that I cannibalized from the dead Sony Vaio we were given (though at first, I forgot to install the ferrite RF choke from the Vaio, which gained me another 20dBm in S/N ratio once I remembered it).
So at last, I have a fully functional laptop that doesn't require a tether. (Though it could stand a new battery; this one's down to 34% capacity.) Victory at last! And I even swapped the smaller of the two memory cards into the externally-accessible slot, so I can push it up to 1GB any time I can get my hands on another 512MB PC2100 or PC2700 module.
(Interestingly, although the spec says it requires PC2100 RAM, the 256MB module that was in the internal slot is PC2700, just like the one originally in the external slot was. The 512MB module I replaced that one with is PC2100, and the CPU happily runs at full speed with it.)
