I'm back, after doing a little more homework.
First off, I was wrong about the 8192e driver, what I wanted was the 8192se. Then I reloaded the kernel source (the tinycore-patched stuff), did the whole kernel-building liturgy, then downloaded (again) and built the rtl8192se driver source from Realtek's site.
Next, it's necessary to copy the firmware images from the Realtek tarball, and put them in the right place.
Finally, I built a .tcz with everything I wanted, and on a reboot, I've got my driver loaded and happy with the hardware, or so it seems. At least, it shows up with ifconfig -a, iwconfig gives information about it, and so on. I haven't yet got it actually get an ip address, so that still to be done, can't be too big an issue.
My thanks to the tinypoodle.