Just an out of the box thought, but if your power steering pump had been running low or dry, maybe it's damaged, and is putting a lot of friction into the turning of the engine, e.g., the power steering pulley shaft is sticking, and initially the starter had to overcome that additional friction, thus the slow initial turn. As the steering pulley starts to move, it loosens up, and the engine rotates faster. You may still have leaks, but check to see how easily the steering pump rotates otherwise you may end up burning out another starter motor.
-Jerry