Well, I guess taking a break from the problem helped me fix it, but I'm not sure how. I came back to my machine, removed the symlink in "/usr/bin/" to "/sw/bin/glibtool" and restored the original "libtool" binary, removed the existing libapreq source directory, unpacked it from the tarball, and started over. This time it worked. Perhaps in all my efforts before I was still linking to something incorrect, but I seem to have Apache::Request installed now. Perhaps, at least, my earlier message will help point other OS X users in the right direction if they make the same mistakes I did.
ky