I like your interpretation. I think that Holden sees that he is over the 'edge' and is no longer a child, expected to understand the complexity of adult relationships and responsibilities when he is not ready or willing to do so. There is the idea of preservation from loss of innocence, but also having to accept responsibility for oneself and one's faults.
I think the "edge" Holden is referring to is the loss of innocence. Once it's lost, you have nothing but experience, and thus, adulthood where everyone is a liar or phony, or both (at least in Holden's view). He wants to save the children, and especially his siser Phoebe from this harsh reality--the real world. He has not found much to be impressed with, and even his favorite English teacher gets a little weird with him.
I asked this question because I am writing an early assigned english paper for university (first year), out of the novels assigned I must write about an unkown theme or symbol that I have created. Personally I think it's a tough assaignment as you have to be a good reader, but I assume my prof just wants the class to really go in depth with our chosen novel. I was wondering if, worded correctly, i could use the interpretation I fabricated as my main topic. The symbol being "the rye field cliff as an analogy for the adult world." Do you think that I have gone in depth enough? That i have demonstarted how much thought I have put into the novel?
Ps. thank you for the comments quite helpful, I guess i should have elaborated a little more as to why I was reading it.