That’s an interesting way of doing it. Never would have thought to do that.
I copied template-example.php and created a new template template-events.php and set that as the template in the TEC setting. Then I added some logic to roots_title() (in /lib/titles.php) to make sure I display the appropriate title on TEC pages. Let me know if you’re interested in this snippet and I’ll create a gist.
I believe this was all I needed to do to get it working but I will write a post about it once the project is complete as I added some customizations to the plugin itself that could be useful to others.