If a rod is held above the event horizon and then slowly lowered down into the event horizon, any part of it that passes through the event horizon will rip apart from the rest of the rod. It doesn't matter what the rod is made of. It's impossible for any bonds to maintain themselves on either side of the event horizon unless they are in free-fall (or close to it).

As a layman I think that if your rocket were to lower a rope towards the event horizon, the rope after it passed through - would start acting like an anchor. You cannot get it out, anymore - you can follow it or let go.

The same would go for your legs. Event horizon is an abstract limit at which not even light can escape. __not even light__. I guess that the point of no escape for your rocket, no matter how powerful it was, was far, far more.

What happens if a contemporary earth rocket would go into orbit around Jupiter? At some level it couldn't get away with its engines. That would be the point of no return. Nothing inherently bad happens, except there is no way to go but down.

The part of the rope within the event horizon would not act like an anchor. It would just immediately rip apart from the rope outside of the event horizon.

Unless the rockets can match or exceed the speed of light, does it matter since only photons can maintain a circular orbit that close the event horizon as was already stated?

(PS: I think that advanced material you're referring to is also known as Unobtainium :)

I think you've reached the point where analogies break down, and you'd have to do the math and physics to resolve your objection.

http://xkcd.com/895/