I agree the foundation of the unforgivable sin is unbelief, but this particular sin has it's own properties.
For example, this sin can only be committed by one who professes to be saved. The Pharisees professed to believe God and believed they were saved, but as we see from Scripture they were far from that belief.
This is what Christ said following the Pharisees claiming that Christ had performed miracles by the power of Satan.
Matt. 12:31-32
"Wherefore I say unto you, All manner of sin and blasphemy shall be forgiven unto men: but the blasphemy against the Holy Ghost shall not be forgiven unto men.
And whosoever speaketh a word against the Son of man, it shall be forgiven him: but whosoever speaketh against the Holy Ghost, it shall not be forgiven him, neither in this world, neither in the world to come."
We see here that any sin can be forgiven, but not when it's committed against the Holy Spirit. This falls in line with unbelief as you have shown.
Paul also twice in his epistles gives the example of the unforgivable sin, both times the Holy Spirit is involved and as you have pointed out, the root was unbelief. But it was a specific unbelief, the rejection or if you will, an insult directed specifically toward the Holy Spirit.
I see this as just another prime example of who the Holy Spirit really is....... God the Almighty.