In no place in the word of God does it say that an Elder is after the order of Melchisedec, or after the order of the Melchisedec Priesthood.
An Elder is after the order of Christ. (Revelation 4:4)
This matter of “priesthood,” since the days of Sidney Rigdon, has been the GREAT HOBBY and stumbling block of the Latter Day Saints.
Priesthood means AUTHORITY, and AUTHORITY is the word we should use.
I do not think the word priesthood is mentioned in the New Covenant of the Book of Mormon. (It’s not.)
Authority is the word we used for the first two years in the church—until Sidney Rigdon’s days in Ohio.
This matter of the two orders of priesthood in the Church of Christ, and lineal priesthood of the old law being in the church, all originated in the mind of Sidney Rigdon.
He explained these things to Brother Joseph in his way, out of the old Scriptures, and got Brother Joseph to inquire, etc.
HE WOULD INQUIRE, AND AS MOUTHPIECE SPEAK OUT THE REVELATIONS JUST AS THEY HAD IT FIXED UP IN THEIR HEARTS.
As I have said before, according to the desires of the heart, the inspiration comes, but it may be the spirit of man that gives it. (David Whitmer, An Address to All Believers in Christ, p. 64)