Hi James,
It seems like your best bet is going to be to use the Default Events Template, I’m not quite sure why the Default Page Template is not working but it must be some incompatibility with your theme.
What you’ll need to do to get up and running with the Default Events Template is one of two options.
1. Add Before & After HTML in Settings > The Events Calendar > Template and include the particular markup (wrapper div’s) from your theme to wrap the calendar. You can likely find this in your theme’s page.php template. Look for what’s missing in the markup when you inspect the page.
2. Edit /wp-content/plugins/the-events-calendar/views/ecp-page-template.php by making a copy and placing in an ‘events’ folder in your theme. Then, do the same thing in that file. Add the necessary HTML wrappers particular to your theme to get the calendar wrapped nicer.
I hope that helps!
– Jonah