It takes bamboo too long to get big? Mine will go to five feet tall by however wide its allowed in a month. You need to keep it in a container (a strong container it won't punch through) though.

Have you considered vines? Even just sprawling, they look very tropical, even something as temperate as clematis or hops.

I was just wondering if you have ever tried growing the perrenial hibiscus. You could leave it in the ground without having to overwinter in the basement. They die back to the ground in winter but come back bigger every year. Mine are over 8ft tall every year. I used to live up north & they will easily overwinter where you live.