How about a Pet, released on a Wednesday, whose sole purpose is to collect tributes at regular intervals?
Upgrades could be based on the time intervals in which the pet would collect tributes. For example…
Level 5 : Auto collect tributes every 6 hours
Level 10 : Auto collect tributes every 4 hours
Level 15 : Auto collect tributes every 2 hours
Level 20 : Auto collect tributes every hour
This would be a major gem sink, now that you rarely get more than 1 pet from a rescue event. Or, offer this for real life money the next day - enough copies to ascend the pet to mythic.