What would you recommend?

Catalyst::Plugin::RequireSSL

Is Catalyst mature enough to be used in such a setting?

Yes.

If not, is there another system that may seem suitable?

Yes, but none as fast as Catalyst:-).

An example:

#!/usr/bin/perl

use strict;
use warnings;
use Catalyst;
MyApp->setup( qw/RequireSSL/ );

My App->config->{require_ssl} = {
             https => 'secure.mydomain.com',
             http   => 'www.mydomain.com',
             remain_in_ssl => 1,
                         no_cache => 1;
};
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Just add this to each controller method:

$c->require_ssl;
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