This is a Moose / Mojolicious program which uses DBIx::Class

Well, that sounds like your problem right there. You also mention in the original post that it is a CGI program, which Moose have been known to attack and bite ;)

First, if it really is a vanilla CGI program, try switching to a persistent environment this will use less memory over time since a lot of Moose and DBIx::Class only grab memory once at compile time and are they pretty reasonable thereafter.

If that doesn't work, or if you already are in a persistent environment. Try swithing Moose to Mouse (or possibly Any::Moose) as that will at least reduce that part of the memory footprint.