that might among other things be used to stop Shai'tan from a stunt like tainting Saidin through Rand touching him..

However, you'll have to come up with something better than just saying "Rand's body will be used to seal the Bore". Be more concrete, because as it stands now, that doesn't seem to make any kind of sense. Forget the themes and such, plotwise how come a dead body be used to mend a hole in the fabric of reality. Really, how would that work?

However, if Alivia severed Rand at the right moment, that would leave him defenseless, to be killed by the Shadow or Fain, and this would fulfill her "helping Rand to die", in a way he could not accomplish on his own (ie: he would still be connected to saidin, even if he let himself be killed).

That bit really isn't bad, and perhaps you're onto something. The body to seal the Bore thing sound ludicrous to me, to be honest. Alivia would take a huge risk to even channel in the Pit, however. What's to stop Shai'tan from turning her to cinder the second she channels?

IMO, the key is that for the Wheel, the Bore does not exist. There's something foreign to the Pattern preventing the Wheel from reverting things to normal. There's a Bore only because Shai'tan holds it open, I think. So, the solution, IMO, is to bring Shai'tan to lose his grip on the Bore. If Rand alone is enough to part the unnatural storm where he goes, bringing Perrin, Rand and Mat together (the three shall be one) and doing something to make Shai'tan lose his grip on the Bore might do the trick. If Shai'tan releases his grip even for a split second, the Bore will be gone, and he will be sealed outside again, without any need for anyone to use the OP to touch him.

It's hard to see how Rand could make Shai'tan lose his grip, however. Capturing Padan Fain and bringing him to SG could possibly do the trick. Fain is terribly dangerous to Shai'tan. The Evil of Fain and the Evil of the DO cannot co-exist in one place, they destroy one another. Faced with Fain at the Pit, the DO might be forced to retreat, and neither Shaidar Haran nor Moridin could do anything, as Fain is as much a peril to them (Moridin was insane to even use the TP at Shadar Logoth, but after the Cleansing and what happened to the city and the Taint he must be more aware of the threat now). Another solution could be to kill Rand with the Shadar Logoth dagger. He would be consumed by its Taint, and Rand is linked to Shai'tan. This could kill Moridin and make Shai'tan retreat from Rand as fast as he can, but perhaps not fast enough. Perhaps the conflagration that results could make Shai'tan lose his grip just long enough for the Wheel to make the Bore vanish.

But I think there's a bit more to it than that. There's Callandor for one thing. I would take it as a given that if Callandor is present at the Pit, Alivia would be the second woman with Rand. I still get the feeling Callandor is a red herring, or a trap. A trap for the Shadow. I think bringing Callandor to SG, and advancing with two women, is the way Rand will fool the Shadow (Moridin, SH, the DO himself) into believing Rand's plan is to stupidly attempt to channel the OP there and touch Shai'tan with it. There's also that viewing of a black hand holding the sword. Shaidar Haran? That sword magnifies the Taint, and that's probably very important. It could mean the Shadow could seize control of it, invest it. If Rand expects it, this could be turned into a nice trap... a lot of TP (thus of Shai'tan himself) invested in the sword as Rand alone holds it, then the SL taint come into play and causes the the big bang, kill Rand and make Shai'tan momentarily lose his grip. Alivia could be there to pierce Rand's side, letting the SL evil pour out at the Pit of Doom. Rand can certainly not expect Nynaeve to accept to do that! Nynaeve would accept to go in the vain (or perhaps not so vain) hope there would be enough of Rand left to heal afterward.