Thinking about my [2] cheat a little further, with a small black hole the time dilation gradient near the black hole is large, so the inner bits of the hyperbol

Thinking about my [2] cheat a little further, with a small black hole the time dilation gradient near the black hole is large, so the inner bits of the hyperbolically-orbiting experimenter will feel a drag compared to the outer bits (relative to the horizon). The "drag" is because the outer parts are winning a race with the inner parts thanks to gravitational time dilation, against a suitable set of local coordinates on the astronaut. If the astronaut is facing inwards with a rocket on his back, then inner bits are liable to be torn off and left behind. [1] The gradient is much lower for a much larger black hole, so this sort of drag becomes apparent ever closer -- or even right at -- the outside of the horizon. For a sufficiently large black hole, dipping one's hands towards the black hole will probably not feel any different compared to deep space, even very close to the horizon. However, one would then expect a short sharp shock dipping one's hand into the horizon. Bye-bye hand. - -- [1] Put the rocket pack on the closer-in side, and the intermolecular forces etc that hold the astronaut into familiar shape will decelerate the whole astronaut along a suitable choice of coordinates. The coordinates you want are probably integral over Fermi normal ones for ever-smaller components, lots of fun to calculate.