How can I move the potion explosion ingredient dispenser?
Yes! Gluing the joints with common Elmer's Glue makes the dispenser sturdy enough to move about when filled with marbles.



Assembled without glue, the dispenser tends to come apart:



Empty the dispenser and turn it over.



Apply glue to everywhere the supports cross each other.  I didn't put glue anywhere it would be visible from the outside:




After drying overnight, it can be filled and moved about without any trouble.  It fits into the storage box that comes with the game.