Mother and daughter; father and son; brother and sister; husband and wife; friend and friend; teacher and pupil. To the varied array of human relationships, the phenomenon and experience of Chassidism has added one more: the bond between the rebbe and the chassid.
What is the nature of this bond? There is fierce love in it, and unquestioning loyalty. There is passion, devotion, admiration, appreciation, awe, mentorship, care, concern, sacrifice. Almost every human emotion is there, in heightened form. (Chassidim even quip that had King Solomon been a chassid, he needn't have resorted, in his Song of Songs, to the example of romantic love as a metaphor for the relationship between G‑d and Israel — he could have used the model of the love between rebbe and chassid.) But can it be described?

Regarding your: "The moment I try to read these articles with the mind of one who's never experienced the connection, it reads like a rave by a celebrity worshipper, or the forgivingly naive gushings of a young newlywed."
I can't imagine any chassid, regardless of the label he's given himself as such, reading a rebbe-chassid story as if he's never experienced such a connection. Could I, for example, read an article that deals with someone's deeply loved mother with the mind of one who's never experienced such a mother-daughter relationship?
Of course, I may have misunderstood you altogether.
I think it’s quite different. The Rabbeim explain this deep bond that has and continues to always remain. The bond beyond the physical boundaries. The very nature of the Rebbes soul being bound up with ours. The lack that occurs in us also occurring in the Rebbeh. There is much more than meets the eyes in this world.