There is kind of a paradox about the space brake idea. At least in terms of the kinds of propulsion concepts we are aware of, the spaceship would have to be spewing exhaust out the tail in order to try to move away from the black hole (or move toward it more slowly than it wants the ship to approach). In real, practical terms, at least as practical as we can imagine, the volume/mass of the exhaust would be a lot. It would make a metric tera-fuck-ton look like a speck of dust in comparison. So, we are dumping unthinkably large amounts of mass into the black hole, which causes its mass, and thus its gravity, to increase, probably at a non-trivial rate. Thus, trying to not fall in would be making the situation worse.
Which leads to another question. Suppose you have a ship that can go really fast by firing a rack of really powerful lasers out the back. So you use this drive to try to brake into the black hole. Photons have no rest mass, but they are still something. So, firing them straight down will dump gazillions of yottawatts into the thing. Photons would somehow raise its energy level – is there such a thing as an energy level of a black hole? What happens to all the massless boson-thingies that plunge into the singularity?