Chris,
The issue is coming from either a third-party plugin or some other site customization. Possibly an SEO plugin or Schema plugin.
If you look at the error for the event you mentioned in the Google’s Structured Data Testing Tool, click on the red error on the event and it will highlight the location on the page where the error occurs (on the right-side).
In this case it highlights, <meta itemprop=”startDate” content=”April 20″>. April 20 is not a valid date format. The Events Calendar is not creating this microdata. Again, some other plugin or customization is creating it.
If you view the page source and search for <script type=”application/ld+json”>, this is the JSON that The Events Calendar generates. Within that JSON you will see the correctly formatted Start and End Dates.
"startDate":"2018-04-20T00:00:00+00:00","endDate":"2019-04-29T23:59:59+00:00"
Unfortunately Google is picking up the malformed meta data first. Not sure why, that’s Google for you.
Hope this helps.