I came up with a strategy for this type of thing working on a project that uses CGI::Application and Template. First, unlike the usual CGI::App style, my runmodes return only raw data structures and I save the template rendering for the cgiapp_postrun phase. When running tests, I can override the cgiapp_postun method and set $ENV{CGI_APP_RETURN_ONLY} = 1. Then I can set up a fake CGI environment, load and run my module directly (without going through a web server) and use stuff like is_deeply to make sure the data structure looks right.

I also have a separate set of tests for making sure the templates render properly.

Also, since my app has a rather large inherritence tree and lots of small subclasses that only override a method or two, I use Test::Class to do xUnit style inherrited tests. That way I can set up a new subclass that might only have a dozen lines of code, and set up its test class to inherrit the six hundred tests from the parent class.