ITOps Automation: Auto-assign issues based on a Opsgenie On-call Schedule

As a service desk team lead, I would like to automatically assign new tickets to the engineer that's currently on-call according to Opsgenie.

A bit of background:

We recently decided to make use of the Opsgenie inclusion into Jira Service Management Cloud to create on-call schedules for our first-line engineers.

I've found a community post suggesting a solution for the problem at hand, where a new ticket in the Service Desk created an Alert in Opsgenie. If the alert was ack'ed in Opsgenie, a comment would be made to the ticket Service Desk containing the username of the ack'ing user. A Service Desk automation rule would then run to assign the ticket to the username mentioned in the comment. It could work, but it would still require our engineers to interact with alerts in Opsgenie. We currently only use Opsgenie to administer the on-call schedule, and we don't need the full-fledged alerts management functionality it provides.