You might want to look at Log::Log4perl. It can do everything you want with a little work:

read contact info from a central file:

Check. You can do something like Log::Log4perl::init('/etc/log4perl.conf'); at the start of your script to setup logging for all modules.

Control how often emails get sent

Write a custom appender and you can make it do whatever you like. Log::Log4perl::Appender::Buffer could probably do what you want.

Optionally override normal warn/die/carp/croak calls

See My program already uses warn() and die(). How can I switch to Log4perl? in the FAQ.

Optionally handle unexpected death as well as die/croak calls

See How can I make sure my application logs a message when it dies unexpectedly? in the FAQ.

Make it so the user can do as much configuration as possible at the beginning

You can do all the configuration in one call at the start.