Exactly what happens if you uncheck “DreamHost Managed” in the web server section of the control panel? Do you have to make your own arrangements for Apache to start?
If you uncheck it, that basically means you are responsible for changes made to the httpd.conf for your VPS. Unfortunately in that case, since you are managing it, it would be out of the scope of our support to help you troubleshoot issues if they arise.
So I’d get to impose some sanity on httpd.conf and e.g. not load both mod_fcgid and mod_fastcgi? Good.