I think that I could possibly accept some form of Inclusivism, but I don't know if I could really apply it to someone who has been exposed to Christ but openly rejects Him; I think it could perhaps only apply to those who have never been exposed to Him.
I'm not sure exposure or lack thereof is enough for us to make such a judgment call. Saul of Tarsus, after lots of exposure to and rejection of the idea that Jesus was the Christ, openly and adamantly rejected Him.
Denying Jesus was the Christ, denying the Son, he was according to the passage from St. John's epistle you quoted previously without the Father: Saul of Tarsus: antichrist! And yet we also know even at the same time God, beyond all time, knew his end from his beginning, knowing his future as St. Paul, even while he was yet in the womb, and He was present there, knitting Him together and holding his atoms in place, with love immeasurable. Such knowledge is for God, I think, not men. Can we truly know that a person "with exposure to the idea of Jesus as Christ" is somehow further from God or hope -even as they exist without the Father, as liar, as antichrist- than a person without such exposure?
This is why Paul understood salvation was by God's mercy -beyond rational expectation or calculation.
 "As a staunch and conscientious Pharisee he was filled with horror at the blasphemous sect that proclaimed a crucified malefactor as the promised Messiah of Israel" (Metzger, NTBGC, 193). Especially absurd and blasphemous to a Jew like Saul was the idea that the Messiah, the Blessed One of God par excellence, would die on a tree as a malefactor, a fate reserved for those cursed by God (Deut 21:23: "A hanged man is accursed by God"). The Messiah "was believed to be the expected leader to victory by battle who's function was to conquer and rule a Jewish empire from Morocco to Indonesia. Crucified Messiahs are paradoxes -hard to sell." ibid). Saul of Tarsus wasn't buying.
The degree to which Saul's zealous leadership was responsible for the severe persecution suffered by the early church is evidenced in the fact that persecution of the church came to an abrupt halt with his conversion (Acts 9:31)!
Acts 22:4-2: "I persecuted this way to the death, binding and delivering into prisons both men and women, as also the high priest bears me witness, and all the council of the elders, from whom I also received letters to the brethren, and went to Damascus to bring in chains even those who were there to Jerusalem to be punished."
 "Who is the liar? It is whoever denies that Jesus is the Christ. Such a person is the antichrist—denying the Father and the Son. No one who denies the Son has the Father; whoever acknowledges the Son has the Father also." -1 Jn 2:22-23