But I couldn't find any other references on Google to people having issues running RecDescent under Mod_perl.

Read the documentation for Devel::SawAmpersand. This provides you with the necessary information that the slides without narration do not.

The problem with mod_perl is that the perl interpreter is re-used for subsequent requests. Everything that is global, is still around after the document has been served to the browser.

Parse::RecDescent will work, and not slower than you're used to, but there may be a significant slowdown for other scripts. To solve this, consider running a dedicated Apache httpd for the P::RD script, or factoring the parsing out of Apache (fork, or communicate with a daemon).