Hi Brian,
Thanks for reaching out! I’d be happy to help with your questions.
I’m not exactly sure what you mean by “push that data to the Calendar” in the context of a widget, but there’s a lot of functions, hooks and filters within our plugins that can be used to create custom functionality. You can find more information on our documentation page: https://theeventscalendar.com/?s=tribe_&submit=Search&post_type%5B%5D=wp-parser-function&post_type%5B%5D=wp-parser-hook
You are correct, custom fields in a Pro feature. Pro also comes with a collection of Events widgets. If none of the widgets do what you need, you may be able to use the code as an example of using the Events Calendar data in a widget.
Hope that helps! Please let me know if you have any additional questions about this.
Thanks,
Sky