I don't see the problem with using cgi-app, it works well and is lightweight (lighter than Catalyst certainly) with lots of useful extensions (and being based on CGI, which is well-known and well-tested, I consider a plus). It also supports being run under PSGI (as do most Perl web frameworks these days). I just converted my application web servers (which sit behind static serving and mod_proxying apache processes) from apache+mod_perl to native perl, PSGI-enabled servers, as most of my apps are based on CGI, CGI::Application and CGI::Application::Dispatch, it was pretty smooth to 'Plack-ise' them. Since CPAN::Forum is not a framework, there is no need for it to be rewritten to use PSGI, even if the author wanted to use PSGI/Plack as 'glue'.
Enough good things can't really be said about DBIx::Class, I use it for all my complicated database apps (for the simple ones I use SQL::Abstract). I doubt, however, that using it would make CPAN::Forum an easy conversion to another RDBMS, or change the default or supported RDBMS to a more cheap hosting provider-friendly option.
All that being said, I don't see why a rewrite of the backend of the forum needs to be considered at all, since it is working.