OP, my emirates flights were massively changed also same as you (SEA-DXB totally cancelled), and this is the only thing that helped:

Go on alaskaair.com, and yourself find something acceptable to you available on emirates awards. The new flight you want to move to must have business class award availability.
Call alaska airlines and give them the exact flight numbers and dates you want to change to.

That is the only thing that helped. The agents themselves were totally incompetent in finding acceptable route offerings.