Hey Geoff,
Thanks for reaching out, and for your interest in our plugins.
Your hunch is unfortunately correct here—we do not have any shortcodes at the moment that would embed the whole calendar into a page or other post type.
There are some methods for inserting calendar content into a post or page, which are covered in this knowledgebase article → https://theeventscalendar.com/knowledgebase/inserting-calendar-content-post-page-content/
But none of those methods are “complete”; i.e., you can only ever embed widgets or shortcodes of the widgets, which are never the full calendar with all of the Pro views and date filters and all of that good stuff… 🙁
Sorry to disappoint! Let me know if this information helps you move forward in your search for the right plugin, and/or if there’s anything else I can try to help with.
Sincerely,
George