Source: This order of prayer is based on an e-mail from Joseph McLellan (graduate of Jordanville, PhD in Slavonic from Brown; currently professor at Princeton), who said it is based on instructions from Fr. Ignaty, former choir director at Jordanville. However, this order is not the same as that which is contained in the printed edition of the Slavonic Psalter, but seems to reflect a local (Jordanville) tradition.
After the usual beginning (see below), we say the first stasis. At the end of the first stasis, we say the Glory..., as indicated, but instead of Alleluia, alleluia, alleluia, glory be to Thee, O God, we say the Trisagion through to the Lord's Prayer. If there is a priest, he says the Doxology, otherwise, we say, O Lord Jesus Christ, Son of God, have mercy on us.
Then, the following troparia, in Tone VI:
O Thou Who alone art by nature the creator of life, O Christ, and art truly an unfathomable sea of goodness, grant entry into Thy Kingdom unto Thy servant [handmaiden], N., who hath now departed, for Thou only art He Who hath mercy and compassion.
Glory be to the Father, and to the Son, and to the Holy Spirit; Both now, and ever, and unto the ages of ages. Amen.
O Lady, who gavest birth unto the Fountain of life, the Redeemer of the world, the Lord Jesus, earnestly entreat Him to grant life unending to thy servant [handmaiden], N., who hath now departed, for thou only art the renowned helper of Christians.
Lord, have mercy. 
Remember, O Lord our God, Thy servant [handmaiden], who hath departed in the faith and hope of eternal life, our brother [sister], N., and, as Thou art good and lovest mankind, pardon his [her] sins and consume his [her] unrighteousness; release, remit and forgive all his [her] sins, voluntary and involuntary. Deliver him [her] from eternal torment and from the fire of Gehenna, and grant unto him [her] participation and enjoyment of Thine eternal blessings, prepared for them that love Thee. For if [s]he sinned, yet [s]he did not renounce Thee and believed undoubtingly in Thee as God: the Father, the Son, and the Holy Spirit, glorified in Trinity, and confessed the Unity in Trinity and the Trinity in Unity in Orthodox fashion, even until his [her] last breath. Therefore, be merciful unto him [her], and impute his [her] faith in Thee instead of deeds and, as One gracious, grant unto him [her] rest with Thy saints. For there is no man who liveth and sinneth not, and Thou, alone, art without sin, and Thy righteousness is righteousness forever. For Thou alone art a God of mercy and compassion, and unto Thee do we ascribe glory: to the Father, and to the Son, and to the Holy Spirit; now, and ever, and unto the ages of ages. Amen.
Then, O come let us worship..., and the second stasis. After the second stasis, we repeat the above. After the third stasis, we do likewise, excepting that, after the Lord's Prayer, instead of the troparia above, we say the penitential troparia appointed after the kathisma in the Psalter. Then, Lord, have mercy  and the appointed prayer. And so for each of the remaining kathismata.