I read Roy Palmer’s book “Zone mind, zone body” some years ago, and I remember that it is nice book with description of many examples.
I guess that “psycho-physical unity” in the AT sense is description of characteristics of what we are, and “zone” is a partcular state of mind which has poise even when the body is very active. So, I think they are different thing. I believe that the AT helps to be in zone (as Roy Palmer), i.e., more practicing the AT, more chance to be in zone.
What makes zone then? Probably particular state of autonomic nervous system, especially a certain high level of parasympathetic nerve, will help to make zone (I guess). If we feel more comfortable, the level of parasympathetic nerve will be higher. If we can make our muscular tension minimum (for movement and activity), the level of parasympathetic nerve will probably be higher also. So, I think that these factors are keys. If we can manage our body and making it less muscular tension and comfortable through controling our use, we may have more chances to be in zone.
It is more difficult for us to control the state of mind. But on the other hand, it is easier for us to control the state of body, because most of our use are by the skeletal muscles which are potentially under our conscious control. So, all we can do is just to manage what we can control to be in comfortable, and to hope to be in zone. I think that the notion of the independence of bodily control from mind may help to be like this.