Try preloading your needed modules in your startup.pl (using mod_perl). These loaded modules are shared now for all apache processes.
You should use Apache2 prefork MPM however, as i found out here: (shared) memory and preloading modules using Mod-perl, and don't have to be reloaded.
Next you can change the apache config, and set the MaxRequestsPerChild to a lower number, so if there are little leaks in a script (i hope not ;-)) the child process is stopped, and memory is cleaned.
next, indeed mod_perl uses more memory, it keeps compiled code in memory, that's what makes it fast.