My walk up success rate is woeful. At best I've been offered the chair in my last half a dozen attempts. But then I typically ask at 2-3 hours before the flight. I suspect at 3-4 hours it would be much better.
The arrivals spa appointment is a particularly elusive animal. I've arrived too early to make an appointment, and at other times found nothing for athe least a couple of hours within 10-15 mins of the desk opening for business.