I have overheard and participated in lengthy discussions on this topic. But with all due respect, there is no need for speculation and philosophizing on the matter. The core question on every chossid’s mind should be “How does the Rebbe want me to approach this situation?” And the answer is that first and foremost, this can only be ascertained through delving sincerely into his words.
The Rebbe prepared us for this situation in his sichos throughout the years. In particular, it appears to me (as I have been taught by my teachers) that according to the principle of “he ruled concerning himself” discussed here, the best guide for a chossid in relating to the Rebbe after Gimmel Tammuz is the sichos that the Rebbe delivered during the years immediately following Yud Shevat. In these sichos (for the Hebrew, see here, here, and here) the Rebbe demonstrates how a chossid should relate to a Rebbe after the Rebbe’s Histalkus, maintaining and even increasing his bond. These sichos have even been translated and released by Sichos In English under the title of “Proceeding Together” (see here, here, and here).
I have pointed out some of these sources on this blog, but there is simply no substitute for thoroughly studying these sources inside. In my opinion, these sources are the “manual” for a chossid in relating to the Rebbe today. I really don’t understand how people who have not learned through these sichos function as chassidim in this time, considering that they lack this crucial guidance. I am not in the least bit surprised when I see people who have clearly not learnt these sichos floundering in confusion.
I do not claim that these sichos resolve every possible question that may arise concerning the relationship of chossid and Rebbe today; however, the core issues are discussed and clarified, thereby providing tremendous strength and encouragement in this time of darkness and doubts. Try it and see!