You don't have to pvp in Cyrodiil at all, the ironic fact about "PvP event" is that all you need to do is to do some PvE quests in PvP location. Depending on faction you have Bruma, Cropsford and Vlastarus daily quests - 9 quests per location per character, meaning you can get up to 162 boxes just from one of those locations, if you decide to do it in the other ones you can triple that number
I'm done with this game because of ZOS pushing us into Vengeance, because they don't know how to fix Cyrodiil.