You need to accelerate to about 42.1 km/s to escape the solar system
Sure, but I said "the Earth". Never the less you may include the Sun, okay. It is 40+ km per second then, to escape the system: a black hole -- our planet, in one direction. You can't in the other, you will stumble into a black hole in other direction.
My point was, we have different escape velocities for different directions, from one point. Don't we?
No, it's the same velocity regardless of direction, because the escape velocity is determined by the potential energy, which is just a number for each point and is direction-independent.
As mister shminux mentioned somewhere, he is happy and qualified to answer questions in the field of the Relativity. Here is mine:
A long rod (a cylinder) could have a large escape velocity in the direction of its main axe. From its end, to the "infinity". Larger than the speed of light. While the perpendicular escape velocity is lesser than the speed of light.
Is this rod then an asymmetric black hole?