I give you my answer. I don’t want you to take as THE answer; it’s simply based on my experience and also seeks to avoid becoming too philosophical and abstract. Thus, I also want to avoid merely theorizing, i.e., to answer you with other AF quotes on the subject.
So, let me first address this other question of yours:
I have had various PCEs: many for an instant or minutes; quite a few for several or many hours; one for several days.
Except when I am having a PCE, I constantly feel that I am not this flesh and blood body only!
That is to say that even if/when I am really enjoying and appreciating this moment of being alive (i.e. applying the method), if I am not in PCE I feel that I am also something else; I feel that I am really something more than just this body: I feel that I am a someone, that I am an identity, that I am a self/me.
Only if/when I am having a PCE that feeling/sensation disappear. I stop feeling like a somebody, an identity, an I/me. I then perceive myself as something, that is to say, I start to perceive what is left: this body only.
So if I’m having a PCE, there would be nothing wrong (to address your thought) with perceiving the body as not me; it just does not happen because the I/me who usually perceives it as such is deactivated!
So, both things you say here
can be in my experience exactly as you describe them, as long as I am not in a PCE. In a PCE these sensations cannot be created simply because the I/me that can create one or the other is deactivated. So if/when the identity is deactivated, what remains is simply the body perceiving itself.
So, you don’t need to be identified with the body to practice the method. In fact, you will feel identified with the self, with your-self (more precisely, you will feel being that identity, you will feel a self, an I/me) in the same way that happens to me while practicing the method (while enjoying and appreciating!) 
The question that I think might interest you is why on earth Richard chose as his method “to enjoy and appreciate”, which to many of us at first seemed like nonsense, which can easily be confused with positive psychology, with mere optimism, with just disregarding whatever is unpleasant in life, etc?
What happens by practicing the method is that enjoy and appreciate is the gateway to induce PCEs when accompanied by other elements such as pure intent, etc. This is what happened to me about two weeks after I started the method, when I was still years away from ceasing to long for this identity (that I still feel I am when not in PCEs) to exist forever.
So I assure you that to begin to successfully practice the method (enjoy and appreciate), and even experience PCEs, does not “depend on being identified with the body”.