I have come up with a partial solution, using a trash can with a handle on the lid that should discourage the reverse Jenga effect, where people try to add things without knocking over the pile. Also a smaller can that makes emptying it easier seems to be helping. But other suggestions are welcome.

I have come up with a partial solution, using a trash can with a handle on the lid that should discourage the reverse Jenga effect, where people try to add things without knocking over the pile. Also a smaller can that makes emptying it easier seems to be helping.