"I don't know that any portrayal of Jesus as a "troublemaker for the Romans" is an accurate one."
You are correct that Jesus' trouble for the Romans did not exist directly per se, but he was trouble for the Romans in that he did exactly what you spoke of -- fomenting rebellion against the Roman puppets and the Jewish religious oligarchy who were put in place by the Romans. Remember, the Jewish leadership in Palestine during the occupation only existed at the pleasure of the Roman overseers. Jesus and His followers represented a threatening counter to their rule and the priestly class of the Temple.
In effect, Jesus Christ was a "rebel" only from the perspective of those elements in the Jewish leadership (primarily the Pharisees and Sadducees) who were bent on toppling the Roman rule.
Jesus Christ came into this world at a time and place that was ideal for the fulfillment of the Law because it was aided by the Roman rule of the entire Western world. There are two reasons for this:
1. Governance by a large empire ensured that His message would be carried far and wide during a very short time.
2. A powerful civil governing authority that subjugated regional religious groups actually helped reinforce the idea of a Christian worldview in a Gentile world. This could not have happened if the basic concept of a small group of "chosen people" in the Middle East had prevailed as God's instruments of human salvation.
The notion that Jesus was a "rebel" falls apart once you step past the Gospels chronologically and see how history unfolded. The Romans sacked Jerusalem in 70 A.D. and destroyed the Temple to quell the uprising by the same Jewish sects that were at odds with Jesus Christ when He was alive.