I have been using Pair Networks for over 10 years and they really are top-notch, though not cheap. They have many CPAN modules already installed including Moose and DBI - see the list here.
While Pair is a great option and it’s nice to reward them for hosting PM, I think that considering what’s installed for Perl while host shopping is a mistake. You should never rely on what the host has for anything except maybe command line work and one-offs. It’s too easy to have your own stable libs and perl and likewise too easy for a host upgrade to wreck your sites and cronjobs without warning. I learned this the hard way repeatedly.