There is no real secret to making this first jump. You simply sprint & jump constantly until you come out the other side. It's pure luck that you actually jump at the end without bumping your head. But you'll need all that speed to make this 6 block jump. When you do finally jump at the end without hitting your head be ready to shift as soon as you hit the ground.
With the 4 pressure plate jumps just go fast & try not to take big angles. Want I mean by that is go in as straight of a line as possible. If you make big turns with your jumps it slows you down. This makes it hard to jump far enough, AND it gives the pistons a chance to hit you.