How can I control the comment counts filtering my CPT replies?

Here are three different methods to modify the trash count, to 999 as an example:

Method #1

The views_edit-comments filter:

add_filter( 'views_edit-comments', function( $views ) 
{
    $trash_count = 999; // <-- Adjust this count

    // Override the 'trash' link:
    $views['trash'] = sprintf(
      "<a href=%s>%s <span class="count">(<span class="trash-count">%d</span>)</span></a>",
      esc_url( admin_url( 'edit-comments.php?comment_status=trash') ),
      __( 'Trash' ),
      $trash_count
    );
    return $views;
} );

Method #2

The comment_status_links filter:

add_filter( 'comment_status_links', function( $status_links ) 
{
    $trash_count = 999; // <-- Adjust this count

    // Override the 'trash' link:
    $status_links['trash'] = sprintf(
      "<a href=%s>%s <span class="count">(<span class="trash-count">%d</span>)</span></a>",
      esc_url( admin_url( 'edit-comments.php?comment_status=trash') ),
      __( 'Trash' ),
      $trash_count
    );
    return $status_links;
} );

Method #3

Here we target the edit-comments.php screen and adjust the corresponding instance of the wp_count_comments() function:

add_filter( 'load-edit-comments.php', function() 
{
    add_filter( 'wp_count_comments', function( $stats, $post_id )
    {
        static $instance = 0;
        if(  2 === $instance++ )
        {
            $stats = wp_count_comments( $stats, $post_id );

            // Set the trash count to 999
            if ( is_object( $stats ) && property_exists( $stats, 'trash' ) )
                $stats->trash = 999; // <-- Adjust this count
        }
        return $stats;
    }, 10, 2 );
} );

Similarly for the pending and spam counts.