If the option is one or the other, I'd go the Seanchan. However I don't think it's going to be some sort of neat, Seanchan, Black Ajah wrap-up, Tower fixed, in which order you like.

I think the Black hunt - whether trying to take Alviarin, or Alviarin trying to take one or more of the hunters will happen just before, or during the attack.

One thing though which tends to get overlooked is in Egwene's dream the Raven's (Seanchan) hit the Tower causing major damage, BUT then fly off. Given the timeline's, I've suspected since COT that they launch the attack before hearing of Turan being trapped between two armies in Arad Doman, and are forced to go save him. With the events in the Prologue I can see this taken further that at least one Raken witnesses Turan's Sul'dam/Damane being toasted so they desperately need more and are forced to bring them from the Tower attack, leaving that to go for now with whatever Aes Sedai they can get out with as quickly as possible.

Which is logically sensible, that there's no point having one large victory if it's at the cost of a large defeat elsewhere, better to take a smaller victory and avoid defeat as well.