This quote from Muhsin Mahdi really encapsulates much of what I've been collecting and alluding to here, the insistence that somewhere out there must be a 1001 Nights, the real version.
"There is widespread resistance to raising and attempting to answer questions such as the following: What is the Nights? How and in what form have the stories survived? In what sense do they form a book? It is human to search for the completion and the end of every affair and to think that one can know the end from knowing the beginning. It is also human to fail to recognize that some things have no known beginning and may not have a knowable end. The desire to know the beginning is thus satisfied by inventing it, and the desire to know the end is satisfied by fabricating it. Such, in any case, have been the human failings from which the Nights has suffered most."
from The Thousand and One Nights (Alf Layla wa-Layla): From the Earliest Known Sources: Part 3 Introduction and Indexes. Leiden, EJ Brill, 1994.