Answer: Unfortunately, Musa acuminata is only hardy in zones 10 and 11 (think southern Florida or California) so it would not survive for you no matter how much mulch you used. Musa basjoo is a hardier banana that should survive for you outdoors in the ground. It will however need a very rich and evenly moist yet well drained soil to do well. It will also freeze back to the ground each winter, so it will not fruit or reach its full potential size.
For tall, large leafed plants with a tropical look, you might consider planting Canna. There are many varieties available with terrific bold foliage in green, purple, and stripes. They also produce bold flowers in pink, orange, red, yellow, or striped patterns. These are grown as annuals in your area but the rhizome (root) can easily be dug and stored each fall for replanting the following spring. They do best in a full sun location with rich, evenly moist soil.
You might also consider yuccas for a tropical look. Yucca filamentosa and named varieties of it should do well for you in full sun and a well drained location.
If the spot is sheltered, you might also consider one of the hardiest figs such as Brown Turkey. Figs have very tropical looking foliage. The fig will probably die back to the ground each winter but will regrow quickly and Brown Turkey should fruit.
Another option for a tropical look is to plant corn; it would give you height and looks quite interesting when planted among other plants.
Yet another way to provide nearby height might be to set a bench or bit of fencing in the desired spot and then plant a vine to grow up it.
Your local professionally trained nurseryman might have other ideas based on a more detailed understanding of the growing conditions where you want to plant as well as your overall design goals. Enjoy your project!
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