I've wanted this for similar reasons. Mostly, because I want oncall engineers to have a standardize escalation for themself, ie email immediately, call 1 minute later and every 2 minutes after that.

Part of the motivation was to give Nagios a small window to autoresolve, and another lesser motivation was that one of our systems triggering pagerduty incidents also emails our support system, and this 1 minute delay helps make sure there's a support ticket by the time the engineer is called.

I'd checkout pagerduty-tools: https://github.com/precipice/pagerduty_tools/

One of the included scripts includes report functionality, but it's a littl less specific than you are looking for. Some clever coding should make it possible though.