After many hours of toil, I finally have Request Tracker up and running on a DreamHost site!
Here's a brief summary of what I had to do:
Install the perl dependencies in my home directory
Build RT with my PERL5LIB environment variable set to use my custom perl modules
Modify the RT scripts to use lib, since suexec prevents the scripts from using PERL5LIB
I still have to set up procmail to pipe incoming mail to the RT mail gateway. I created a separate shell account for that, but it shouldn't be so bad (I hope).
Two things that would have made installing RT easier:
1) If the perl modules were installed/updated
2) ScriptAlias support
Now here's the bad news. RT is slooooooooow. I don't think it can be helped though, since it is running on a shared server after all. Also, because of the lack of script alias support, I am forced to use /rt/mason_handler.cgi/ instead of /rt/.
Well, if anybody is interested, I can post more details about it. Thanks for reading!