“Jesus died a Roman death, he was not stoned as a Jewish criminal or blasphemer. Why then are the Jews given the blame for his eventual crucification?”

Because the Jews were allowed to have one criminal released to them, as was the custom. They choose an obviously guilty man to go free so that Jesus would be crucified.
“Why were Jesus’ followers allowed to continue in Jerusalem, more-or-less without persecution?”
They hid in the Upstairs Room until Jesus sent the Holy Spirit to be their guide. Then they began to build the Church, and they were persecuted then.
“Jesus was Jewish, by all accounts a religious Jew. Why then did his followers, not many years later seem to have renounced Judaism and Jewish practices and in the Gospels blamed the Jews for Jesus’ death?”
The Jews did not believe Jesus was the Messiah. Jesus died so that the Jews would not have to continue sacrificing, etc., to appease God. The Jews rejected Jesus…there is a passage in the Bible somewhere that says, “He was rejected by His own.”…Under the new covenant, we have a Saviour, Jesus, who died for our sins. The Jews still practice all the rules and regulations because they rejected Jesus.