My advice would be to download /home/username/perl5 so that you have a backup, then completely delete /home/username/perl5/lib/perl5/* from the server. Then, create a cpanfile that lists every module that you need and upload that to your project directory, then (because I'm assuming you have local::lib active already) download the cpanm tool and use that to install all your modules listed in the cpanfile.

# locally
rsync -avxH mywebhost:perl5 .
rsync -av cpanfile mywebhost:my_project_directory/
[download]

# on web host
ssh mywebhost
rm -r ~/perl5/lib/perl5
mkdir ~/perl5/lib/perl5
cd ~/my_project_directory/
curl -L https://cpanmin.us | perl - App::cpanminus
cpanm --installdeps .
[download]

This is the standard recipe for re-installing the modules that your project needs on a new server. (or on a server where perl has been upgraded across major versions)

If you don't have shell access on the server, just run those lines from "system" in a CGI script, though this is admittedly harder.