How did you split the distribution into 240k files?
Newer BSD based systems have a -b option to split that allows them to split files on arbitrary byte boundaries.
Here is an example from /usr/src/Makefile.
bin-tarball:
(cd ${DISTDIR}; \
tar cf - . \
gzip --no-name -9 -c | \
split -b 240640 - \
${RELEASEDIR}/tarballs/bindist/bin_tgz.)
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