Some options:

• FCGI or CGI::Fast can allow you to move to a persistent model with only minor changes to your existing code - although you will need an FCGI-capable webserver. See also mod_perl
• Don't load all the modules in all the scripts. If you've been clever in your design then it is likely that most of the scripts will only need a fraction of the modules.
• If some modules are only needed by some execution paths in a single script then only load those modules on demand in those execution paths.
• Use lighter modules to begin with. You don't say which modules you have currently used but avoiding the monsters (Moose is a good one to ditch for instance) can make a huge difference.