I don't see the Jordanville Prayer book as being in any way influenced by Protestantism. This very same prayer, in a slightly different translation is also in the St. Tikhon's Press Prayerbook, called Orthodox Daily Prayers. It is included as the 9th prayer of Morning Prayers on pp.19-20 as follows:
My most merciful and all-merciful God, O Lord Jesus Christ! In Thy great love, Thou didst come down and become flesh in order to save all. Again, I pray Thee, save me by Grace! If Thou shouldst save me because of my deeds, it would not be a gift, but merely a duty. Truly, Thou aboundest in graciousness and art inexpressibly merciful! Thou hadst said, O my Christ: "He who believes in Me shall live and never see death." If faith in Thee saves the desperate, behold: I believe! Save me, for Thou art my God and my Maker. May my faith replace my deeds, O my God, for Thou wilt find no deeds to justify me. May my faith be sufficient for all. May it answer for me; may it justify me; may it make me a partaker of Thine eternal glory; and may Satan not seize me, O Word, and boast that he has torn my from Thy hand and fold. O Christ my Savior: save me whether I want it or not! Come quickly, hurry, for I perish! Thou art my God from my mother's womb. Grant, O Lord, that I may now love Thee as once I loved sin, and that I may labor for Thee without laziness as once I labored for Satan the deceiver. Even more, I will labor for Thee, my Lord and God Jesus Christ, all the days of my life, now and ever and unto ages of ages. Amen.
I think this is one of the most beautiful prayers in all Orthodoxy. It is certainly one of my personal favorites. I think it most probably originated somewhere in Slavic Orthodoxy because I have never found it in Greek Orthodox or Antiochian Orthodox prayer books. But that's OK, because no two prayer rules anywhere are going to be exactly the same. Even in Tsarist Russia, prayer rules varied considerably from monastery to monastery. And most prayer books are simply adaptations and usually abbreviations of some monastery's prayer rule.
I think the theology in the prayer is solidly Orthodox and not Protestant in the slightest. Note the following:
1. At the very beginning of the prayer Christ is addressed as "God." How many Protestants start their prayer with "O Christ our God ..."? None I've ever met.
2. The second sentence of the prayer mentions the Incarnation, "Thou didst come down and become flesh in order to save all". When do Protestant ever mention the Incarnation (except maybe at Christmas)? Calvinism is also excluded here because Christ comes to "save all" not just the "elect."
3. Don't let the Protestants make you afraid to talk about the Grace of God. Orthodox firmly believe in the Grace of God. However, remember that Orthodox define "grace" very differently from Protestants. For Protestants, "grace" is God's unmerited favor bestowed on sinners. In other words, you could say that grace, according to the Protestant definition, is a change within God Himself, because God changes how he sees us. I call this the "worm with a Jesus mask" theology. According to this view, under the condemnation of the Law, God sees us all as vile sinners worthy of hell, worms, as it were. But under "grace" God doesn't see us as we really are anymore. When God looks at us under grace, He sees "Jesus" . Hence my description of their view as "worm with a Jesus mask" theology. The Orthodox view of Divine Grace is much different. We view the grace of God as Divine Energy, an Energy that most specifically comes to us through the Holy Mysteries and Sacraments of the Church. And that Divine Energy or Grace of God enters into us and transforms us and gives us the ability to cooperate with God and do good works.
4. Lastly, note that the prayer calls for "laboring" or working for Christ all the days of our lives until death. It doesn't view salvation as past event that has already been obtained (Protestant style) but something that we are laboring for and hope to attain with the grace of God and His mercy.
I hope this helps.