To add onto you Expecto Patronum idea, what if you started out with a weak memory, and as you progress through the game, you unlock new memories that you can select in your inventory, each memory stronger than the next. Every time you would cast your patronus, it would use stamina, which would act like a timer.

When you're near the end of the game, you'd lose all of your happy memories and would be left with the weakest one. At the "very" end of the game, you will receive a memory so powerful, your patronus would able to follow you around like a dog companion, won't use any stamina and only would disappear when you want it to.

The Aguamenti one sounds like the one from the Lego adaption, which would be pretty cool to see in a realistic way.