Just a minor point, for I believe the status of being published is less definitive to the canonicity issue then it may seem. It is very much circumstantial affair - if there were no shortages of paper in the post-war England, or if prior to the war the reader of the publishing house have seen the whole bulk of materials sent in, not the fragments of lays only, or if the post offices worked less or more
bona fide and lost or did not loose (this latter we do not know, of course) one or more letters in correspondence of Tolkien with his publishers, if, if, if, if etc, the:
A. Published texts may have been different
B. There may have been more of them
Or, to put less words around it, the origin is what matters - i.e. the work should be written by Tolkien, but it's status as of being published or not is of less consequence
Or, I'm more or less in for historiography issue again - i.e. it matters if the source is genuine, it does not were it bound in leather and gold in its time or daubed on a hut wall.