Re: my boat dances on a ball
Stern-to. Center of pressure (wind) will be farther "aft" (the new aft - bow of the boat which is now the end away from the bouy) causing things to steady out. Has worked well for me but I've never done it longer than overnight.
Obviously this won't always be a good idea even if it works, considering how the mooring line will ride off the stern, weather, idiots in the moorage freaked out by a boat moored facing downwind, etc.