The exosphere? Not even our shuttles fly that high, let alone most nations of Earth. If they can get that high they won't need a SE. Earth orbit is halfway to anywhere in the solar system.

The first ribbon would require enough material for two SEs. Subsequent SEs would have no material loss and could be deployed at full strength.

As far as a lunar slingshot is concerned, I don't see why it has to be on the pole. Sure it would require less energy to keep the rotation going, but it's speed would vary due to earth's gravity. If one was on the front side it could use earth's gravity to cancel droop. One on the backside could use "centrifugal" force to cancel droop.

I do have trouble visualizing it, though. If there are two opposing cables, would they be rotating in the same plane (disc shaped), or at an angle to each other (cone shaped)?

Is there a limit to the number of cables you could have on one hub?

Could payloads be accelerated with energy generated by the tether as it passes through the moon's magnetic field? Could the same be done for an earth sling shot, or would the cable just burn up?

Personally, I think building a lunar slingshot would violate some international law because of it's potential use as a weapon. That would be unfortunate, especially considering it's impracticallity compared to current weapons with much more controlled lethality.

CNTs are probably the best conductors that can ever be possible on a nanoscale level at 0.4 milliohms. I think the Edwards report said that a 20 ton ribbon would be 5 megaohms, but I suspect the resistance will come from mostly from the non-CNT material and coating.  CNT power cables could theoretically withstand current densities of a gigaampere per square cm (an electrical cord the width of you finger could power an entire city). They also are extremely thermal conductive and are hoped to achieve higher levels of heat dissipation for microprocessors. This could be good news if you are worried about ice forming on the cable.

Some amount of discharge may occur in the radiation belts as one is positive and the other negative. Check out HiVOLT.

I would like to know if anyone has theories on how well the elevator would stand up against solar flares or positive lightning.

Actually, I think slack would cause the counterweight to gain altitude and then slowly creep westward. All you would have to do is accelerate a tad.