WP_QUERY with group by with custom fields

(Revised answer)

So after discussing via the comments, what you really need is a custom ORDER BY clause, which in WordPress post queries (WP_Query), you can set the clause via the posts_orderby filter just like you can set custom GROUP BY clause via the posts_groupby filter.

The order that I need is June – 2019 | May – 2019 | April – 2019 |
April – 2019

If the value of the meta eventMonth is always in this format: {month name} - {4-digit year} such as June - 2019 — note the dash/hypen which shouldn’t be “–” or any other special characters, then the following ORDER BY clause can sort the posts in the order specified above: (the WordPress table prefix is assumed as being wp_ and this example sorts in descending order)

ORDER BY STR_TO_DATE( REPLACE( wp_postmeta.meta_value, '-', '1,' ), '%M %e, %Y' ) DESC

And the PHP code:

1. Modify the ORDER BY clause:

   add_filter( 'posts_orderby', 'query_order_by_filter', 10, 2 );
   function query_order_by_filter( $orderby, $query ) {
       // Modify only if and when applicable.
       if ( 'eventMonth_date' === $query->get( 'orderby' ) ) {
           global $wpdb;
           $order = $query->get( 'order' );
           return "STR_TO_DATE( REPLACE( $wpdb->postmeta.meta_value, '-', '1,' ), '%M %e, %Y' ) $order";
       }
   
       return $orderby;
   }
   

2. When making your post/WP_Query queries, set the orderby parameter to eventMonth_date:

   $args = array(
       'meta_key' => 'eventMonth',
       'orderby'  => 'eventMonth_date',
       'order'    => 'DESC',
       // ... other args.
   );
   $query = new WP_Query( $args );
   

   PS: If you use get_posts() instead of new WP_Query(), make sure to set suppress_filters to false.