Our auditors will want to see what was deployed, who deployed it, and what tickets justified the deployments. How can we report on that info and export it for the auditors' review?

The History tab in Essentials will contain this information.

All noteworthy deployment information, like the questions down below, can easily located within that tab.

Even deeper than that, you can sort through your own deployment history and your team's deployment history for EACH deployment YOU have access to.