OMGWTFBBQSPEEDYDASHBOARDS.php

<?php
/*
 * Plugin Name: Remove crazy counts slowing down my dashboard
 * Plugin URI: https://pmgarman.me
 * Description: Those comment counts are such a pain when you have a lot of comments
 * Author: Patrick Garman
 * Author URI: https://pmgarman.me
 * Version: 1.0.0
 * License: GPLv2
 */

// Remove unmoderated comment counts from the admin menu
function pmgarman_unmoderated_comment_counts( $stats, $post_id ) {
	global $wpdb;

	if ( 0 === $post_id ) {
		$stats = json_decode( json_encode( array(
			'moderated'      => 0,
			'approved'       => 0,
			'post-trashed'   => 0,
			'trash'          => 0,
			'total_comments' => 0
		) ) );
	}

	return $stats;
}
add_filter( 'wp_count_comments', 'pmgarman_unmoderated_comment_counts', 10, 2 );

// If running WooCommerce, remove their filter so that nothing funky goes down
remove_filter( 'wp_count_comments', array( 'WC_Comments', 'wp_count_comments' ), 10 );

// Remove order count from admin menu
add_filter( 'woocommerce_include_processing_order_count_in_menu', '__return_false' );

@tnorthcutt finally pulled in your change :D