I'm pretty sure what you want *is* Apache::PerlRun. You don't give any clear reasons why it doesn't do what you want. AFAIK, this is pretty much how PHP achieves it's faster processing that vanilla CGI, it only loads one instance per webserver. (Of course, a lot of PHP configurations actually run in vanilla CGI mode, so they don't get this performance benefit).
in reply to More than mod_cgi less than mod_perl.
As you point out, to gain a further increase in speed requires pre-compiling code. This will only work properly if the code is written properly (primarily that it deals with the potential pitfalls of persistent variables).
One option between Apache::PerlRun and full mod_perl is Apache::Registry, although this may require some modifications to existing CGI scripts (but not quite as much as migrating to a mod_perl handler).
If you're really concerned with performance, then you're always going to struggle unless you have flexibility around your webserver's configuration. For the 'masses', they probably could/should be using Apache::PerlRun. But even if they're not, I doubt the performance of their applications is actually an issue.