HAVE: Arundo donax
The giant reed is mistaken for bamboo, used for flutes, and has escaped into the wild.
I have many rhizomes as this has grown over 12 feet tall in my yard. In my experience, it does NOT spread out of the area in which it is watered.
Right now, I'm interested in a Chorisia speciosa sapling, pup from a large specie of banana, or Buddha belly bamboo.