The confusion only arises with the reading weakness of the modern English. So, it is rather the problem of the modern English readers, than the language and teachings used by men of God. It is clear that the KJV used "faith of Christ" literally, because at that time people were more used to such genitive construct.
If it is "faith of Christ" which really could be translated as "faithfulness of Christ" ... then to me there is more security of being found in the righteousness that comes from God. If my faith is responsible for me to gain access to the righteousness that comes from God, that has human condition problems.
I'm afraid, your security is founded on the misconception that it stands upon God's work or faithfulness (something that is universalism a similar idea which shuns the responsibility of man). The genitive in Greek is to be understood as objective that may be possessive or subjective to the referent (it is always your faith in or about something). The faith of Christ the criteria that saves you which you exercise, it is your faith or submission to him, it is the new dispensation of righteousness, Rom 3:22 "the righteousness of God through (your) faith in/of Jesus Christ for all who believe". Faith of Christ is the same thing as faith in Christ in every instance including Philippians 3:9. It is the Christian faith.
I will quote from the book, Going Deeper with New Testament Greek, Merkle, Plummer for some reference examples:
When a genitive noun is attached to a head noun having an inherent
verbal quality (e.g., love, anger, desire), then the genitive often
functions as the subject of that verbal idea. For example, if the
expression “love of God” could be rearranged to “God loves x” and
maintain accurately the author’s intent, then “of God” is a subjective
genitive. One of many examples in the NT can be found in 2 Cor 5:14,
which states, “For the love of Christ controls us” (NASB; ἡ γὰρ ἀγάπη
τοῦ Χριστοῦ συνέχει ἡμᾶς). The head noun ἀγάπη has an inherent
verbal quality, and we are thus predisposed to read the genitive
attached to it as a subjective or objective genitive. Context makes
clear that Paul is speaking about Christ’s love for his people, so τοῦ
Χριστοῦ would be the subject of the verbal idea “love”—a subjective
genitive. Whether a given genitive is a subjective or objective
genitive (or some other kind of genitive) can be inferred only from
the context.
ἡ πίστις σου σέσωκέν σε (Luke 18:42) Your faith has healed you
The person Jesus healed exercised faith.
ἐν τῇ ὑπομονῇ ὑμῶν κτήσασθε τὰς ψυχὰς ὑμῶν (Luke 21:19) By your
endurance gain your lives
Jesus is calling on his hearers to endure.
αὕτη ἐστὶν ἡ μαρτυρία τοῦ Ἰωάννου (John 1:19) This is John’s testimony
John the Baptist testified.
τίς ἡμᾶς χωρίσει ἀπὸ τῆς ἀγάπης τοῦ Χριστοῦ (Rom 8:35) Who can
separate us from the love of Christ?
Paul is not speaking of our love for Christ (which would be an
objective genitive; see below), but Christ’s love for us.
I disagree with the interpretation that those references are subjective genitive in the above quotes, but all of them are objective genitive. God's love cannot constrain anyone, he is already sovereign, but our behaviour is constrained only by our own freewill. If only we love Christ, then we can constrain ourselves; this is what is meant by "love of Christ controls or constrains us"; the context is clear (in 2 Cor 5:14 or Rom 8:35) it is always talking about our faithfulness. Paul says nobody can separate him from following and loving Christ, even oppression, persecution and death, he and the likes, would never leave Christ. It is meaningless to even think of the possibility of Christ or God ceasing to love us; and why would Christ separate himself from loving us when we are oppressed and persecuted for him?
Some examples of objective genitive: (your) Zeal of God (KJV and other old versions) Rom 10:2 is translated "zeal for God" in the modern versions, there is no difference; testimony of Christ, that is the Christian message (1 Cor 1:6) "testimony about/concerning Christ" in the modern versions.
A great verse to illustrate the distinction between the subjective and the objective genitive is Acts 9:31: “So the church . . . had peace, being built up and walking in the fear of the Lord [objective genitive] and in the encouragement of the Holy Spirit [subjective genitive], increased in numbers” (ἡ μὲν οὖν ἐκκλησία . . . εἶχεν εἰρήνην οἰκοδομουμένη, καὶ πορευομένη τῷ φόβῳ τοῦ κυρίου καὶ τῇ παρακλήσει τοῦ ἁγίου πνεύματος ἐπληθύνετο). The church feared the Lord (objective genitive), and the Holy Spirit encouraged believers (subjective genitive).
ἡ δὲ τοῦ πνεύματος βλασφημία οὐκ ἀφεθήσεται (Matt 12:31) but the
blasphemy against the Spirit will not be forgiven
The Holy Spirit becomes the object of blasphemy.
ἔχετε πίστιν θεοῦ (Mark 11:22) Have faith in God
Robertson comments, “we rightly translate [this phrase] ‘have faith in
God,’ though the genitive does not mean ‘in,’ but only the God kind of
faith.”
διὰ τὸν φόβον τῶν Ἰουδαίων (John 7:13) for fear of the Jews (ESV)
In Acts 9:31, both genitives are objective where they "walked in the fear of God and in the comfort of the Spirit". God did not fear them, nor did the Spirit unilaterally comforted them. They were solely responsible for walking in the fear of God and comfort of the Spirit, otherwise they wouldn't have had any reward if they were passive puppets in a puppet show. Ps 36:2 NASB "Transgression speaks to the ungodly within his heart; There is no fear of God before his eyes".
Job 4:6-8 NASB
6"Is not your fear [of God] your confidence, And the integrity of your ways your hope? 7"Remember now, who [ever] perished being innocent? Or where were the upright destroyed? 8"According to what I have seen, those who plow iniquity And those who sow trouble harvest it.
If you avoid relying on the modern misleading translations, it will be beneficial to restore the proper English and improve your understanding of the language. If we study the context we would know that blasphemy of Spirit cannot be blasphemy done by the Holy Spirit. Faith of God cannot be a faith exercised by God, or God's faithfulness. Nobody is saved because of Christ's faithfulness, but only by his own faith; the sacrifice of Christ is described as the grace of God. Christ's faithfulness is never in question.
Romans 3, 10 and Phil 3 shows that the righteousness of God is the requirement for righteousness from the subjects. When the law covenant has been finished, and one still relies on it, rejecting the faith (in Christ) covenant, he is establishing his own righteousness against God's. God's acceptable standard of righteousness is on the basis of faith of Christ. The faith concerning Christ. You can simplify it as "faith in Christ", but it will hamper the readers to be familiar with the linguistic nuances. It would be superfluous to talk about God himself practising righteousness and faithfulness, when he is by very nature holy and truthful.
Faith of God cannot be translated as faithfulness of God. Faith of God refers to the required faith from us. That is the new covenant requirement of justification and righteousness. God has always been faithful, but the faith-in Christ covenant is a new requirement that replaces the Mosaic law. This is the whole message of the Gospel of grace. The righteousness of God is the new grace covenant that has been revealed, the new standard of righteousness apart from the law of Moses. Romans 1:17, 3:3, 3:21.
Romans 3:3
For what if some did not believe? shall their unbelief make the faith of God without effect? (KJV)
What if some were unfaithful? Does their faithlessness nullify the faithfulness of God? (ESV)
Gal 2:20 I am crucified with Christ: nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh I live by the faith of the Son of God, who loved me, and gave himself for me. (KJV)
The context and overall harmony of the scripture severely refutes the "faithfulness" 'modern translations' which are erasing the requirement to have faith in God by turning it into God's own faithfulness and actions, as subjective genitive. As long as writers like N. T. Wright, and NET Bible are gaining popularity, it is clear that in the next couple of decades, all the references of faith in Christ will be removed. At first, they started with erasing the necessity of the commands of God for us; and when that was not enough, they had to reduce the requirement of faith as well, since that too may lead many to the righteous works of God. There is a serious need to defend the traditional translations by learning languages. As you have rightly observed that the idea of Christ's faithfulness as opposed to our faithfulness is quite appealing, as it rids of our responsibility and eventually gives all licentiousness and universalism.
A solid foundation on the harmony & background of scripture is a great strength to understand such text.
Matt 5:20, Matt 5:46-48, Matt 6:33 Matt 16:27 Matt 18:3
Acts 10:34-36
Rom 2:6-16
Rom 6:16
1Cor 7:19
2Cor 5:10
1Pet 1:15-17
Rev 20:12
Rev 22:11-12