What was the least important reason for Henry's break with Rome?

Becau he did.

Also the two important reasons were economics and politics. The least was religion. He used it as an escuse to the kingdom when he actually just wanted to start a new Church so that he could divorce Catherine of Aragon, marry Anne Boleyn as she was pregnant at the time. Henry thought it could be a male heir so he needed to make it legitimate as he was having an affair with Anne Boleyn.

However he actually married Anne Boleyn secretly on the 1st of January 1533 when Anne was 3 months pregnant because he was still actually married to Catherine. Once he divorced Catherine he married Anne again when the whole country knew that they were in love.