So this suggestion is going to sound familiar because it's a feature that is in a LOT of other games (or something similar to it). Monster cards.

Monster cards are cards that monsters drop (duh). They are either dropped with a small % chance at random or at set intervals depending on the game you play. Because of the ever-increasing nature of this game I feel like set intervals would allow for a predictable increase over time but random intervals would also work.

The main benefit of monster cards would be a direct increase in damage done to that specific monster. This would most likely be a % base increase (1%? 5%? 10%? Whatever feels right for how rare the drops are.) There could even be different tiers / rarities of cards like common, uncommon, rare, epic -- each giving you a different % base increase damage done to that specific monster.

Of course, cards would only drop while you are online killing monsters so this would encourage active play (as opposed to just sitting offline and checking it every hour).

Along with the monster cards, we could get a card album that would showcase the cards we've gotten along with images of the monsters they drop from. There could be other stuff like concept art or descriptive text for the monster which would help establish the lore/world of the game.