Firstly, if Jesus is God, it is of course impossible for Him to blaspheme against His own law.
Secondly, Jesus did not overtly claim to be God directly and consequently inevitably stumble the lost sheep of Israel that He was sent to. He answered the question:
The high priest said to him, “I charge you under oath by the living God: Tell us if you are the Messiah, the Son of God.” - Matthew 26:63 NIV
“You have said so,” Jesus replied. “But I say to all of you: From now on you will see the Son of Man sitting at the right hand of the Mighty One and coming on the clouds of heaven.” - Matthew 26:64 NIV
Which was not a direct claim to be God, so the response:
Then the high priest tore his clothes and said, “He has spoken blasphemy! Why do we need any more witnesses? Look, now you have heard the blasphemy.” - Matthew 26:65 NIV
Was an error in law and resulted in a miscarriage of justice.
In that conext, there is a sense that you're right (just not the way you mean it), it is definitely not 'Just' that Jesus died in this way, it's actually the very epitome of Grace.
Grace is God acting in a way that transcends the principles of justice and Christianity just doesn't make sense without understanding that.
6 You see, at just the right time, when we were still powerless, Christ died for the ungodly. 7 Very rarely will anyone die for a righteous person, though for a good person someone might possibly dare to die. 8 But God demonstrates his own love for us in this: While we were still sinners, Christ died for us. - Romans 5:6-8 NIV
EDIT in response to OP EDIT:
Why this is not 'trickery', is that it was prophesied before-hand and for those who earnestly desired to look into these things, they could search the scriptures and find them out. Nicodemus as a member of the ruling council would have been challenged by the things Jesus said, but ultimately, he was not offended - instead he placed his faith in Jesus as the Christ and refused to vote in condemnation with the other council members. Although Jesus was a stumbling-block to the Jews (no Christian denies this!) - the choice between being broken on him (and receiving salvation through repentence and faith) or being crushed by him (judged and excluded from the house of God because of a rejection of the Son - whoever rejects the Son, rejects the Father also) is a real one.
The suffering Messiah is typified throughout scripture from the death of righteous Abel to the death of Zechariah the son of Berakiah - all the Prophets and the Law speak to it.
In the same way that God used the (real) injustice of Jesus' death to work the salvation of all mankind; he also used the (imagined) injustice of the Jews stumbling over Jesus as the Christ to further His purposes also - the rejection by (most of) the Jews opened the way for the gospel to be preached to the Gentiles (as was prophesied also).
To characterise God's plan in these respects as 'Unjust' is a category error - it is only possible to view God as unjust from man's perspective, but justice is not applied from man to God, but from God to man. Men might feel that God acts unfairly towards them, but they are wrong if they assert that those feelings are an accurate reflection of reality.