Technically speaking, in classical GR if you begin at any point inside the event horizon of a black hole, your entire future light cone is also contained within

Technically speaking, in classical GR if you begin at any point inside the event horizon of a black hole, your entire future light cone is also contained within the event horizon. That means that a black hole event horizon truly is "uncrossable" (as you phrase it), not just "inescapable". (The Newtonian analogy of escape velocities doesn't really capture the details of GR in this case.)