Weird they would let you install Perl but not additional modules.

It it is possible to repackage Perl yourself. A few years ago, I did that with StrawberryPerl.com (note .com not .org).

As I recall, I used the "PortableZIP edition". I unzipped it, ran the post-unzip scripts, "installed" needed CPAN modules, then zipped it into a new zip file.

It is also possible to create an MSI installer if you need to. I used nsis.sourceforge.net to create one. Unfortunately, I don't remember the details, but it wasn't hard to do.

I've never created an install package for Linux despite Linux being my primary platform, so I can't help you with that.