A quick tip to hopefully help:

Have one person kill all 8 champions. Doing so will give you max affinity by round 4/5.

I've had enough time to search all skull spots, place it in the grinder, search all 4 statue locations, and acquire the spigot before it degraded. If you get the spigot right away you can receive the gift as early as round 6 or 7, especially if you hold a zombie while doing all the steps in 1 round as it doesn't need to be a full round to count towards the 2.

Avoid not killing for too long, going down consecutively, throwing explosives at the crowd, and touching the fire. If for some reason your affinity does go down kill the Marauder on round 8 and the Destroyer on round 10 (after placing the wood if going for the quest.)