The solution to the concept of a great apostasy, in my opinion, is NOT converting everyone to the LDS Church. Rather, it is enlightening everyone with the principles of the Gospel of Jesus Christ - even if that means never mentioning Jesus to some but instead using their own terminology and common beliefs to accomplish the same objective.
Jesus actually didn't establish a church during his ministry. He didn't have to do so; he was his own church, in a way - a classic itinerant preacher. Once he was gone, however, establishing a church became absolutely critical to spreading what he taught ("the Gospel") to the whole world. That "humanization" of principle was the beginning of apostasy, since it introduced mortals into the transmission of immortal principles - and we still are involved in the work of getting back to the ideal and the pure, even within the LDS Church.
One of the reasons I love the Allegory of the Vineyard in Jacob 5 is that is describes, in simple, clear and unmistakable terms, the condition of apostasy as an ever-present, even pervasive condition that will not be conquered until the very end. In my opinion, the Great Apostasy hasn't ended; it simply has been tackled in a different and more comprehensive way.