Unless she's become suicidal and wish the final death which I seriously doubt (that's not at all the impression she gave in the last books, even in her WH POV - she's not as much of a wreck as you think, IMO. Her hatred for Rand keeps her spirits up), Rand is about the last person she would reach out to. It's Moridin she needs to make herself invaluable to.

As others have pointed out, there was a big clue in Shaidar Haran's conversation with Graendal: someone else has been given the opportunity to do to Rand what he wanted Graendal to accomplish. The epilogue sort of reveals who that "someone else" is. It might have been Demandred. but it's Cyndane. Shai'tan might have offered her her freedom if she succeeds and controlled herself, and the final death if she failed, or killed Rand.

Even if Mierin somehow got into her mind to abandon the Shadow, which for a Chosen is hardly possible - Shai'tan can find them anywhere, the only way out appears to get killed with enough balefire so he loses your soul... she would still be corrupted to the bone, utterly selfish, barely sane, and in a general way an evil woman. Jordan has pointed it out: Mierin Aronaille was ripe for the Shadow's plucking long before the Bore.