That probably won’t happen. You need to change factions to get all the dyes and we’re not all coordinating an order. Then, the only reward you’d get for making one faction win every time is… the chance at upgrade materials from deconstructing and some furnishings. And the furnishings are useless if you don’t like that faction (or if you don’t do housing, or if you do housing and don’t have a use for faction banners).