You might want to consider trying your luck with the fast fruiting variety. This means you have to play with time a little here. You can grow a banana and grow it indoor until it's too big for the pot. At the first sign of warm weather in late Spring or early Summer, bring the plant out and plant it in the ground in a sunny spot. Water, feed it regularly and mulch the soil to promote maximum growth in that growing season. Some bananas I have planted that have fruited quickly are Rajapuri, Apple Banana and Praying Hands. However, both Apple Banana and Praying Hands are large plants. Only Rajapuri is a small variety--up to 8 ft tall. I know the Dwarf Cavendish is a smaller variety too, but I'm not able to get it to fruit after three years even in FL. There might be some other smaller and fast fruiters. Maybe some others here who have experience with them can post. There's a likelihood you might get fruit in the first growing season outdoor, but again with bananas, there's no guarantee. My Rajapuri has for the past couple of years been consistently throwing out fruit every six months.

I would think many kinds of banana trees can fruit there, only problem is they will never fully ripen or grow to large size because of winter. Even over here in NorCal z9b the banana's barley get as big as there gonna be before winter sets in. Although they do get very large, they never get ripe on tree. As for growing them outside it is very possible. I am sure you can leave them in ground all winter long, yes they will look dead, but they will come back each spring,( or at least they do here in cali). I would try that with apple and lady finger banana types. Its worth a try. Let me know how they do, good luck.