Good question. I am not an expert in this in any way. I'd think that you have to have dampners in the lattice of the crystal. The only way that works is to dope the lattice with either another 4 valence element, like silicon, or to dope the carbon itself with something. The only think I can think of is to modify the isotopes to be VERY heavy which is obviously therefore radioactive and would need to be replaced a lot. If you used silicon dope then you'd reduce the interatomic strength and therefore make the rope possibly too weak to be used.

I thought that the whole point of carbon nanotubes was that they are the only thing with the 'pull strength' (forgetting the term here) that could withstand the tension. If you weaved them, then you would rely on the Van Der Waal forces to keep the tubes together which is much weaker. Also you have to contend with the phonon interactions, anything tangential to that 'plane' has no effect on the strength, you have to be a part of the lattice to effect things.

Then again, I don't do research in this area.