Bryn, there’s no need to use the_widget() to display events. Events Maker provides a number of fuctions to help you out.

Take a look at that secion of documentation http://www.dfactory.co/docs/events-maker-plugin/functions/ and em_display_events() and em_get_events() especially. First one is used for automated display (like in Events List WIdget), second one works almost the same like WordPress native get_posts() – you can use it to get events, then make a loop to customize the display.