Instead think of it as a festival mechanic that gives your whole community a year long buff, but requires them all to gather for a feast. This remains ambiguous as to what is being worshipped, and introduces an interesting mechanic, which are the stated design goals of the devs.
You could basically use the farming UI. So a three year cycle, but instead of crops you once per year pick a seasonal festival and place it anywhere in that season.
Whole village stops and gathers for the celebration, which will attempt to consume large quantities of gathered particular resources to determine buff size. The religious workers gather these goods.
I think a subtle advantage of this mechanic is emphasizing the seasonal rythmn of the game, a sort of yearly reset point. It will be best watching everyone stream back to work fully fed. You could even use the spare resources from having everyone do nothing in the same place to go through and optimize job assignments for everyone, or something.
Possible ideas for the seasons.
Winter: Consumes firewood to prepare. Eat meat and preserves. Buffs 1-25% preservation and 1-25% resistance to disease.
Autumn: Consumes wood to prepare. Eat veges and bread. Buffs 1-25% extra output for processed wood items.
Summer: Consumes iron to prepare. Eat fruit and beer. Buffs 1-25% extra output for processed metal items.
Spring: Consumes stone to prepare. Eat berries and cheese. Buffs 1-25% extra output for food and clothes.