The kjv makes it clear that it’s the faith of Christ, not our faith in Christ, that saves us.
Maybe consider generative case when differentiating between faith in and faith of Christ? "In", is the preposition we use in English, as in the KJV and others where faith in Christ appears, and means we believe Jesus. The generative case in the Greek uses "of" is idiomatic as far as the common (Koine) Greek is concerned.And as such is in every sense stating the same thing as is meant by, faith in Christ. "Of", in the Greek idiom, faith of Christ, the object, Christ is that which the faith refers to.
It should be said also that the phrase, faith of Christ, does not consistently appear in the KJV. The translators for the KJV version didn't appear too concerned about there being a difference in actual meaning.