An everlasting priesthood is gone, as it is now not in use. The priesthood is still available to the decedents of Arron and will be functioning when the third temple is built in Jerusalem. The only problem is that you don’t know who has the everlasting priesthood. I isn’t the LDS either.
Exodus 40:12 And thou shalt bring Aaron and his sons unto the door of the tabernacle of the congregation, and wash them with water.
Exodus 40:13 And thou shalt put upon Aaron the holy garments, and anoint him, and sanctify him; that he may minister unto me in the priest's office.
Exodus 40:14 And thou shalt bring his sons, and clothe them with coats:
Exodus 40:15 And thou shalt anoint them, as thou didst anoint their father, that they may minister unto me in the priest's office: for their anointing shall surely be an everlasting priesthood throughout their generations.
Your own quote proves that it was the Aaronic Priesthood that was being mentioned. It was an everlasting priesthood to Arron and his decedents. Unless you are of the tribe of Levi you do not have a right to the priesthood.
There was no anointing of Melchizedek. There is only one Melchizedek priest and that is Jesus. See Hebrews where it states that it is an unchangeable priesthood, meaning it is not transferrable because Jesus never dies again and he is the holder of the Melchizedek priesthood.
Hebrews 7:20 And inasmuch as not without an oath he was made priest:
Hebrews 7:21 (For those priests were made without an oath; but this with an oath by him that said unto him, The Lord sware and will not repent, Thou art a priest for ever after the order of Melchisedec
Hebrews 7:22 By so much was Jesus made a surety of a better testament.
Hebrews 7:23 And they truly were many priests, because they were not suffered to continue by reason of death:
Hebrews 7:24 But this man, because he continueth ever, hath an unchangeable priesthood.
1 Peter 2:9 is saying all believers are a royal priesthood and Revelation 1:5 and 6 is written to and about the saved. The royal priesthood is the only priesthood that Christians hold.
1 Peter 2:9 But ye are a chosen generation, a royal priesthood, an holy nation, a peculiar people; that ye should shew forth the praises of him who hath called you out of darkness into his marvellous light