The ultimate source of the problem was that when I was building 5.10, I called Configure -- as I have always done -- with -de to accept all defaults and skip all prompts. Well, there's one prompt for the directory for architecture-specific libraries whose default value was:

/usr/local/lib/perl5/site_perl/5.8.8/i686-linux/
[download]

... which was the directory that Synaptic and apt-get were complaining about.

So the fix was to: (a) clear out all PERL5LIB settings from by .bashrc file, log out and back in; (b) rebuild Perl 5.10, starting with Configure and responding to prompts manually -- including one at which I said do not use a previously used Perl 5 configuration settings file.

The end result was a purer Perl 5.10. Today Synaptic prompted me to upgrade the cupsys server program. This failed the first time through (which was before I had reinstalled 5.10) for the same reason as cupsys-client did the other day. But after the reconfiguration and rebuild, apt-get was apparently satisfied, because cupsys upgraded without a hitch.