Never use the system's users to authenticate web apps. That's a high security risk and even if everything is encrypted via SSL you're still open to careless users writing their passwords in insecure places. And a persistent hacker could use the web interface to guess user passwords (90%+ of user-picked passwords are trivial) and then attack your system.
Any good reason not to use apache? Apache will do all the serving for you and, through mod_perl, you can still program everything you need in Perl. I never tried mod_perl and DAV integration but Apache::DAV seems to be worth trying at least.