Thanks to the tips received here, I got the compilation to work.
I had to download the configure, Makefile and Makefile.in from
the version of zlib in the opendarwin.org CVS repository, and the
order was a little different...

./configure -s
make install
make test

but the results look good! New libs in /usr/local/lib and sym-linked
from /usr/lib, with the original Apple library saved as a *.apple file.

Now on to the next great adventure...