I now believe that when you pray, offering those prayers up to specific players will yield differing results. By offering my prayers up to the ancient RNG Satan Moarsi, I obtained equally ancient and powerful luck. By offering prayers to Wutan, I got EVERYTHING BUT Ardisia Bride. And by finally offering my prayers to Hungry Hunter, who's aim was the Yandere & Loli Bride, I obtained my long awaited Ardisia OTL.
By that logic, since my primary aim is the Shrine Maidens, prayers offered to me during that event will (hopefully) increase your luck and chances to obtain the Shrine Maidens of Anemone, Dianthus and Lycoris (& probably drain my own luck in the process ).