Howdy Nathan!
That’s totally doable. You can rearrange items by modifying our template files. Even better you can put those modified templates inside of your theme or child theme, that way your changes persist even after updating the plugin.
Checkout our Themer’s Guide for a detailed walkthrough on creating those overrides. The file you want to override is single-event.php. Once you get inside you will see how everything is laid out. It is pretty easy to just cut/paste something to move it.
Does that all make sense? Will that work for you? Please let me know.
Cheers!
– Brook