In my view your idea that Min's Viewing about Alivia helping Rand to die is fulfilled by letting herself killed by Seanchan, so that Gawyn can take Mat's medallion from her - which Alivia for some reason will get from Elayne, who for some reason got it from Mat, because apparently both don't need it (but why would Gawyn take it then anyway? he doesn't know that it stops channeling) - and go on to kill Rand (who has no other guards around?) is simply too far-fetched for me. Min's Viewing clearly implies a more direct help from Alivia in Rand's death, IMO.

That then Nynaeve also has to rip out Rand from TAR seems highly unlikely as well, because it seems - like in Birgitte's case - to be a short-circuiting of the Pattern, which isn't supposed to happen. If the Dragon is needed, he is spun out.

Also, as said, the Heroes waiting in TAR are dead (even if not as dead as others), while a Hero, who is ripped out of TAR, is alive. Thus, Rand wouldn't be alive and dead at the same time, but first dead and then alive.

But there is of course the possibility that the Aelfinn's prophecied "death" would be fulfilled if Rand e.g. just has to be in a deep coma so that he appears to be dead to others, while he is actually still alive. The Prophecies are often not completely literal, e.g. Rand wasn't literally blind as the end Prophecy of TGS.