Short version:
What criteria should I use to evaluate possible candidates for a Perl \"app server\" (mod_perl replacement)?
Starman is a High-performance preforking PSGI/Plack web server that may be used in that context. It's easy to build a REST application that serves stateless JSON objects (this is a simple use case).
Starman is a production-ready server and it's really easy to install a set of Starman instances behind a reverse-proxy (this SO question may helps you), for scaling purposes