You do not need to anger the Brotherhood in order to finish with the Minutemen. You just need to get kicked out of the Institute. I finished the game via the Minutemen route and I was still friendly with the BoS and Railroad at the end of it.
I just waited until Father gave me the quest "The Battle of Bunker Hill". Then I didn't warn anyone about it, went there and let the synths go free and killed the courser (only kill Institute members during this battle if you really have to - ignore everyone else). Then, when Father asks to see you on the rooftop, tell him what you did and call him crazy - that'll get you kicked out of the Institute. Then just go and talk to Preston and the rest plays out from there.
Edit: Its a very quick and lame ending though!