My stats for the past few days show that there is not a whole lot of interest in the subject of Elias! But I'm still into it, so here I go again.
My eye was drawn to the subheading on page 85 of the JS manual, which reads, A person who has the spirit of Elias has a preparatory work assigned to him by the Lord. Now, we Mormons often apply the title "Elias" to John the Baptist, as is done here in the manual. And Joseph Smith taught that his own ordination under the hand of John the Baptist constituted the Spirit of Elias. But we don't generally apply this title to anyone else. This subheading in the manual suggests that anyone who undertakes a preparatory work in a gospel context has the Spirit of Elias. I wondered if these words were really representative of what Joseph was teaching. So I went to the full text of Joseph Smith's March 10, 1844 discourse, which can be found here. The sermon was delivered on the Nauvoo temple grounds and was reported in several different sources: the Wilford Woodruff journal, James Burgess notebook, Franklin D. Richards "Scriptural Items," Joseph Smith diary (Willard Richards), Thomas Bullock diary and the John S. Fullmer papers. The version in the JS manual comes from Wilford Woodruff, who recorded it in the greatest detail.
The subject of Joseph's talk was to show the differences between the work, spirit, and calling of Elias, Elijah, and Messiah. Joseph describes the spirit of Elias as being a preparatory work, and gives the example of John the Baptist. The Baptist's mission was a true representation of the spirit of Elias, because it was a "going before" of another important work. 
After perusing the discourse, I decided that the manual was justified in giving the doctrine of Elias a wider application than I had previously supposed. Joseph said that "it was called the doctrin of Elias even from the early ages of the world" and applied to Aaron, John, Philip, and others. Joseph also told his audience that it is necessary to know who holds the keys of power and who does not, or we are likely to be deceived. A scriptural example is given wherein Joseph gives a unique exegesis of Acts 19:
Paul when he came to Corinth found certain disciples and asked them if they had received the holy ghost since they bleived, and they said we have not so much as heard of the holy ghost and with what surprise says he unto them. unto what were you babtised and they said unto Johns baptism. not so not so my friends if you had you would have heard of the holy ghost but you have been duped by some designing knave who has come in the name of John an imposture. how do you know it Paul? why John verilly babtised with water unto repentance, always telling the people that they should beleive on him that should come after him. he would babtise with fire and with the holy ghost.
Thus those who were doing a preparatory work would not transcend their bounds and would clearly point the way toward the greater work they were sent to advance. Joseph felt that it was important for his audience to know how to distinguish who had the Priesthood of Elias, for "when any man comes among you saying I have the spirit of Elias you can know whether he be true or fals." It sounds as if Joseph was expecting many men to come along claiming the Spirit of Elias!
Perhaps we as a Latter-day Church should be exhibiting more of the spirit of the Elias than we presently realize.
Not included in the manual, but vital to understanding the doctrine of Elias are the spirit, power, and calling of Elijah and Messiah, which Joseph next expounds:
...the spirit power & calling of Elijah is that ye have power to hold the keys of the revelations ordinances, oricles powers & endowments of the fulness of the Melchezedek Priesthood & of the Kingdom of God on the Earth & to receive, obtain & perform all the ordinances belonging to the Kingdom of God even unto the sealing of the hearts of the hearts fathers unto the children & the hearts of the children unto the fathers...
Joseph told his LDS listeners that they were to use the power of Elijah to redeem their dead and to connect themselves with their fathers. The sealing power was used a bit differently in the early days of the Church to form connections between priesthood holders. In this discourse, we can see Joseph's understanding of this sealing power. He tells the brethren to have their sons and daughters sealed to them first, and then seal themselves to their fathers. They should be "crafty" and seal all they can on earth, and these sealings would be in force in the heavens. In this way, the Spirit of Elijah is used to make their calling and election sure.
(In his sermon, Joseph also makes it clear that the power of Elijah may be used by a righteous priesthood holder to seal his enemies or the unrighteous up to the damnation of Hell!)
Finally, the doctrine of Messiah was mentioned. Elias would prepare the way, Elijah would build up the kingdom, and then Messiah would come to his temple. "The Spirit of Messiah is all power in Heaven and in Earth--" Joseph said--"Enthroned in the Heavens as King of Kings and Lord of Lords." Then he ended his sermon with a promise to treat upon the Spirit of Messiah at some future time.
It seems to me that Joseph's purpose in preaching the doctrine of Elias, Elijah, and Messiah was to show his people how to participate themselves in the spirit and calling of the work. I think that a teacher who is well-versed in the teachings of Joseph on this subject might rightly emphasize the spirit of Elias as it relates not only to John the Baptist and to Joseph Smith, but to individual priesthood holders in the classroom.
Now, I'd like to address my final thoughts to how this relates to women, since 50% of those who will hear this lesson in the coming weeks will be female. Joseph had an audience consisting of many women, yet he seemed to address his remarks mainly to Priesthood holders. I often wonder how much he intended to include women in this group, since he may have considered temple-endowed women who were married to priesthood holders as participants in that priesthood.  Be that as it may, the discussion on pages 86 and 87 of the manual quite glaringly leaves women out of any direct involvement in the administration of the Gospel and the spirit of Elias. However, perhaps there is precedent for inclusion. Often, when we speak of the spirit of Elijah, we refer to genealogy and temple work and encourage women to be earnestly involved in this work. In the same manner, might we not sanction the participation of females in the work of Elias? Women can effectively prepare the way for the coming of the Messiah in much of their family and Church service.
 As an aside, Woodruff quotes Joseph saying, "John the Baptist he Came balling through the wilderness prepare ye the way of the Lord." The Burgess version recounts, "he came bounding out of the wilderness saying repent ye for the kingdom of heaven is come unto you." I think it is possible that Joseph was using the word, "bawling." The quote as it appears cleaned up in our manual is, "He came crying through the wilderness, 'Prepare ye the way of the Lord...'"
 This advice led to the practice of the law of adoption, whereby a man could have any number of men adopted to himself as his sons for eternity. For example, in June, 1896, Wilford Woodruff gave a synopsis of his work in the ministry since 1834: "I officiated in Adopting 96 Men to Men." (Wilford Woodruff's Journal, 1833-1898, typescript, edited by Scott G. Kenney, 1985, Vol. 9, page 408) In another synopsis for the years 1834-1885, he revealed: "I had 45 Persons Adopted to me." (Ibid., Vol. 8, page 352) Utah historian Hubert Howe Bancroft gave this information about the law of adoption: "The father may be either younger or older than the son, but in any case assumes the character of guardian, with full control of the labor and estate of the adopted son. Many young men give themselves over to the leaders as 'eternal sons,' in the hope of sharing the honor of their adopted parents." (History of Utah, page 361)
 For example, Joseph Smith to the Relief Society on 28 Apr 1842 “gave a lecture on the priesthood shewing how the Sisters would come in possession of the privileges & blessings & gifts of the priesthood & that these signs should follow them, such as healing the sick, casting out devils &c. & that they might attain unto these blessings….” (Book of the Law of the Lord, (Joseph Smith’s journal) 28 April 1842; also in Dean Jesse, ed “The Papers of Joseph Smith, Vol 2, 378-79.)
Also: “…What was the power of Melchizedek? ‘Twas not the Priesthood of Aaron which administers in outward ordinances, and the offering of sacrifices. Those holding the fulness of the Melchizedek Priesthood are kings and priests (or “Queens and Priestesses“) of the Most High God, holding the keys of power and blessings.” (Joseph Smith, TPJS, 322)