Brakes Pulling

"WHAT" brakes? Drums all around? Disc/drum? Disc/disc? It helps if we know these things. Since you talked about adjusting, I'm assuming drums all around. Pulling with drum brakes, especially hard and fast as you describe, can be perfectly normal. That's the nature of the beast. They "RARELY" actuate at exactly the same time, because of their fairly primitive nature. They work well, but "sometimes" that's just "how it bees". Have you made sure the pads the shoes ride against on the backing plates have been greased? A lot of people leave that out and that's one BIG thing that can sometimes make them hang up for an instant and cause a pull.