Hello @Jamie Taylor ,
What your asking is possible. Within Jira I normally have setup folks so that Epics are in a Jira Project of their own and linking Stories, Tasks, Bugs, etc. to them from other Jira Projects. On the Board of each Project linked to these Epics you have to include the Jira Project that houses the Epics so that they will show up in the left-hand Epic pane of your selected Project Agile Board you wish them to be visible in. You can also do the same sort of technique by adding the project or projects where the Epics reside to the Project's Agile Board filter so that these Epics show up on the left-hand Epic pane.