I throw with my right and fair lead the line out of the cube with my left hand which is ready to work as a brake. If I need to brake, it's generally done by gripping for a fraction of a second and immediately letting go to slow the bag down considerably, but still left hand as a fair lead. I think the "letting go" keeps the branch wrapping away.
I've benefitted more from this technique than suffered from it when a snarl comes out of the cube. Oh, wait, on second thought, that's never happened to me. Not ever.