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.