You're all forgetting the BG had a deadly weapon available the whole time, his car. The BG was in effect "brandishing" a deadly weapon every moment he was driving that aggressively. Is it the law written that way? I don't know, it's still the truth however.
I've been in this situation from the outside (seeing it happen) and called 911 from the car.
The police had me tail the aggressor (they saw it as that important) until they could take over. The person was pulled over and had multiple charges laid against them at that point.
While I talked to the LEO's they were very happy that they had been called and were able to act before there was a physical confrontation.
You acted completely correctly, and with restraint, once cornered. You may want to think about calling 911 when the trouble starts if it happens again.
Gaily bedight, A gallant knight In sunshine and in shadow, Had journeyed long, Singing a song, In search of El Dorado