Reader Misty shared the following information with me, which I'd never have thought of. Now, this method may not be for everyone (probably not even for myself) but it's an interesting (and some - probably even most - may find it morally wrong) idea if nothing else.
Basically, you book a Wyndham Hotel Webrate using a Mastercard or Visa Gift Card that has only a couple of cents left on it. Misty reports that Wyndham does not charge the full amount immediately, and only checks if the card is valid.
Then, after securing the reservation, you'd file a claim for a free room. If you get it, good, but if not, you can basically let the reservation slide. Tell the hotel you're not coming, and if they try to charge the card, they'll be denied.
This method is clearly against countless terms and conditions, and of course we will not condone ripping off hotels intentionally, but this evidently does happen and is a preferred method for getting Wyndham BRGs approved. We'll leave this up to your own moral judgment as to whether this is wrong for you to do.