It took Rand and Co. 14 days to travel from Rhuidean to Cold Rocks Hold. Not 3-5 days. Also, no way to tell if time is wonky specifically in the ter'angreal or if it was just an effect of the shield that was once on Rhuidean and is no longer, but the fact remains that there is over a month between Rand's epiphany and Merrilor. Aviendha was not to Travel directly to Rhuidean, but Amys told her to return quickly once she had passed through the columns.

Aside from that, we know from the wolves that there is no future for Dark Rand. If Rand had not had his epiphany on Dragonmount, he would have destroyed the Pattern. One path leads to the Last Hunt; the other path leads to nothing.