I think a great idea would be the ability to have as an option the ability to chose one of the Giants as you "main" Giant, tho once chosen, would be a permanent fixture (except perhaps some new cards, perhaps one allowing you to re-pick, or another allowing you to be randomly assigned a giant.)
Doing actions related to your giant would grant small bonuses, plus will allow glitch to have random giant dedication days, like an random hour every game day (one giant per day), where people affiliated with that giant have chances to get some of their actions for free during that time ( no energy/mood loss for harvesting/ mining/cooking/ repairing etc)
Keeping your giant happy (regular donations) will result in better bonuses, while not donating may result in random "grumpy" acts - somethings breaks sooner, something takes a lil more energy etc.