Thanks almut. I was more focused on the debug from HTTP::DAV vs the underlying LWP::Authen::Negotiate. With LWP debug enabled, I get the following output:

LWP::UserAgent::new: ()
Setting auth details for default, default to myusername,mypassword
new_resource: For myurl, creating new resource
LWP::UserAgent::request: ()
LWP::UserAgent::send_request: PROPFIND myurl
LWP::Protocol::http::request: ()
LWP::UserAgent::request: Simple response: Unauthorized
LWP::Authen::Negotiate::authenticate: authenticate() version 0.06 call
+ed
LWP::Authen::Negotiate::authenticate: target hostname myhost
LWP::Authen::Negotiate::authenticate: GSSAPI servicename HTTP/myhost@m
+ydomain
LWP::Authen::Negotiate::authenticate: Miscellaneous failure
LWP::Authen::Negotiate::authenticate: No credentials cache found
Unauthorized.
[download]

Based on the debug, it looks like the credentials are not getting passed. At the very least, it gives me another layer to dig into instead of banging my head against the wall with HTTP::DAV...