Hi Ian.
https://wordpress.org/plugins/event-rocket/ has the shortcode functionality like you requested.
For the URL filtering idea, you CAN accomplish this by leveraging our hooks.
I’d suggest taking a look through /wp-content/plugins/the-events-calendar/src/Tribe/Query.php — for example tribe_events_pre_get_posts
If you wanted to create your own loop/list of events, then check out tribe_get_events.
I hope this information gets you going.
Feel free to share any snippets you figure out for others to possibly benefit from in the future.
Thanks!