How I got it working
It turns out that I didn't even need to edit lilo.conf (which was a good thing, because I couldn't access either drive for some reason when I did). I did the following things:
1) Recompile the kernel. I made IDE/ATAPI CDROM support a module (effectively removing it from the kernel, since I haven't loaded it) while adding SCSI CDROM support, SCSI general support, and SCSI emulation support. (I also had to enable loopback device support so I could mount my mkisofs output, but that wasn't neeeded for the SCSI emulation.)
2) Move my /dev/cdrom and /dev/cdrw links to /dev/sr0 and /dev/sr1.
Sure, they're both handled via SCSI emulation now, but that's okay - there was so little configuration needed that I could easily change it back if it became a problem.