Nobody in their right mind has been using CGI::Fast directly for years - we've done it via adapters through e.g. Catalyst::Engine::FCGI for Catalyst and equivalents for other frameworks.
PSGI is just a means to present various HTTP bearing things to the app - in fact the FCGI.pm maintainers all now deploy their applications via Plack::Handler::FCGI.
All perl frameworks of note now have support for PSGI, and Catalyst is dumping its engine modules in favour of Catalyst::Engine::PSGI - we've been heavily involved in improving the Plack ecosystem to ensure that'll be a sane choice.
There's plenty of assurance that it's stable enough.
Go DotCloud for forward thinking choices here.