Instead of loading apache for each php call, why not have a few PHP FastCGI instances running? They're lighter weight than apache+mod_php and you don't have to wait for them to load for each call?
FastCGI is worth looking into - a lot of popular webservers support it, and it's less of a complete model change than switching to an event-based system (e.g. node.js) or an MVC framework.
* Or SCGI, which is a newer, simpler design with similar goals.