PERL5LIB='/v1/data/site_perl' perl -MCPAN -e 'install Log::Dispatch'
Another strategy to consider is to simply build a complete Perl installation in your local directory -- then use that perl's CPAN utilities. They will already have all your own paths built-in. This is the way I tend to do it.
I believe CPAN.pm likes to call a lot of sub-processes for various tasks, and these end up starting new perls, which will not inherit your -I flag. Instead, try setting a PERL5LIB environment variable, e.g.