Example code to sync a subscription to a specific date. All the good parts are thanks to @peterwilsoncc, all the bad parts are my own. This is not intended to be a complete and working snippet. Instead, treat it as a guide to what needs to be changed for syncing a payment date.

subscription-sync.php

<?php
/**
 * Plugin Name: WooCommerce Subscriptions Date Sync
 * Plugin URI: 
 * Description: Sets the start date of a subscription to September 13, 2013
 * Author: Peter Wilson
 * Author URI: http://peterwilson.cc/
 * Version: 1.0.0
*/


if ( ! defined( 'WCS_DATESYNC_STARTYEAR' ) ) define( 'WCS_DATESYNC_STARTYEAR', 2013 );
if ( ! defined( 'WCS_DATESYNC_STARTMONTH' ) ) define( 'WCS_DATESYNC_STARTMONTH', 9 );
if ( ! defined( 'WCS_DATESYNC_STARTDAY' ) ) define( 'WCS_DATESYNC_STARTDAY', 13 );

class WCS_Datesync {
  
  public $start_date;
	public $current_date;
	public $days_until_start;
	
	function __construct() {
		$this->init_dates();
		
		add_filter( 'woocommerce_subscriptions_calculated_next_payment_date', array( &$this, 'calculated_next_payment_date' ), 10, 6 );
		
		add_filter( 'get_post_metadata', array( &$this, 'filter_post_metadata' ), 10, 4 );

		add_filter( 'woocommerce_paypal_args',  array( &$this, 'paypal_standard_subscription_args' ), 11 );

	}
	
	function init_dates() {
		$start_date = &$this->start_date;
		$current_date = &$this->current_date;
		$days_until_start = &$this->days_until_start;
		
		$hour = 12;
		$minute = 0;
		$second = 0;
		$month = WCS_DATESYNC_STARTMONTH;
		$day = WCS_DATESYNC_STARTDAY;
		$year = WCS_DATESYNC_STARTYEAR;
		
		if ( $year < 100 ) {
			$year = $year + 2000;
		}
		
		$start_date = mktime( $hour, $minute, $second, $month, $day, $year );
		$current_date = time();
		$days_until_start = floor( ( $start_date - $current_date ) / ( 60 * 60 * 24 ) );
		
		if ( ( $start_date < $current_date ) OR ( $days_until_start < 0 ) ) {
			$start_date = time();
			$days_until_start = 0;
		}
	}

	function calculated_next_payment_date( $next_payment, $order, $product_id, $type, $from_date, $from_date_arg ) {
		$start_date = &$this->start_date;
		
		if ( $next_payment < $start_date ) {
			$next_payment = $start_date;
		}
		
		return $next_payment;
	}

	function filter_post_metadata( $meta_data, $object_id, $meta_key, $single ) {
		
		$meta_type = 'post';

		$meta_cache = wp_cache_get($object_id, $meta_type . '_meta');

		if ( !$meta_cache ) {
			$meta_cache = update_meta_cache( $meta_type, array( $object_id ) );
			$meta_cache = $meta_cache[$object_id];
		}
		
		if ( $meta_cache['_subscription_period_interval'] > 0 ) {
			// it's a subscription
			$meta_cache['_subscription_trial_length'][0] = $this->days_until_start;
			$meta_cache['_subscription_trial_period'][0] = 'day';
		}

		if ( !$meta_key )
			return $meta_cache;

		if ( isset($meta_cache[$meta_key]) ) {
			if ( $single )
				return maybe_unserialize( $meta_cache[$meta_key][0] );
			else
				return array_map('maybe_unserialize', $meta_cache[$meta_key]);
		}

		if ($single)
			return '';
		else
			return array();


		return $meta_data;
	}

	function paypal_standard_subscription_args( $paypal_args ) {
		
		if ( ( $paypal_args['cmd'] == '_xclick-subscriptions' ) AND ( $this->days_until_start > 0 ) ) {
			// it's a subscription and we're trialling it
			
			$paypal_args['item_name'] .= "–";
			$paypal_args['item_name'] .= "Your subscription begins on ";
			$paypal_args['item_name'] .= date( "F d, Y", $this->start_date );
		}
		
		return $paypal_args;
	}
}

$wcs_datesync = new WCS_Datesync();

Has this been tested with WooCommerce 3.0+?

How do you use this?

I need to sync all orders on a to a single Thursday every 4 weeks. I've searched the web high and low and this is the only resource that seems to offer hope... can anyone give me some basic pointers on how to deploy it?

@stephenclark2000 did you find any solution?

This plugin is a great option: https://shopplugins.com/plugins/woocommerce-subscriptions-schedule/

(I'm not associated with it, I just know that it works)