OK. I talked to one of the physicists who is on the LHC machine advisory committee about the magnet incident, and specifically asked him how they joined the bus bar to the magnet leads. Turns out, it is soldered! It's just normal solder of a copper bus bar onto a copper lead, but embedded in the copper are lots and lots of niobium filaments. So the idea is that when the leads and bus bars are cooled to liquid Helium temperature, the niobium filaments have zero resistance, and thus this is where the current likes to go, as it is a current divider that is zero resistance vs. low resistance, so where possible, all current goes to the niobium. And the small bits where the current must cross solder and copper boundaries have such a low resistance that it doesn't present much of a voltage drop even at very high currents.
The reason it is done this way is that, apparently, there is no way to join niobium to niobium for a super conducting joint. If it isn't cast or machined as one continuous piece, then, no dice. So they embed niobium filaments (wires) into copper and join it in the usual ways.
As for magnet damage, it is too early to tell for sure, but it is looking as if one of the magnet coils was indeed damaged. And, also, I was right about the bus bar exploding / vaporizing! That must have been something. Crazy the amount of stored energy involved here.