You might find it strange getting some input from someone in zone 4, but I have grown the green and red varieties of ensete for about six years now. The green I have grown from seed and the red from nursery plants. Each Fall I dig them up, pot them in 15 gallon pots, and when I bring them inside, either keep them in sunlight and heat, or cut them back and put them in an unheated, unlit storage room in the basement. I have cut off all leaves, cut the plants back to a 3 foot stump, and let them sit all winter with only watering them maybe once until Spring. They will always grow new leaves from the crown, or center of the stump in the Spring when I bring them back in the heat and light. Where you live in New Orleans (I wish I had your climate), you can simply cut off the torn or broken leaves, and it will continue to grow from the central part of the plant. I now have a 5 beautiful red ensete plants in my living room (A frame house with a two story living room with lots of glass windows). The tallest is now 12 feet high and reaches up to the second story of our room. Good luck!

Kevin

Kevin, Thanks for the answer. I want to cut it back short not only for the torn leaves, but also because it's getting too tall. I think I'll try cutting it to a stump & see what happens.

If they get too much cold and freeze you take a very sharp butcher knife and cut them off near the ground at an angle to keep them from rotting. They are easy to cut while green. The stalk can be cut up into small pieces while still green. They get quite hard after they dry out. They will grow right out the of the same stalk and they will look much better next spring.

Thanks Wally, that's exactly the info I was searching for.

If the leaves are green at all, even if they are shredded, leave them alone! Once the leaves are obviously dead, slice them off close to the stalk; the rest of the leaf will eventually brown down to the ground level and pull off easily when they are ready. If you get freeze burn on the whole top of the plant, you can cut the tops away in stages. Stop when you get to anything that looks live. The burned stuff will still insulate the rest of the stalk's interior, and will eventually peel away and can then be removed.
Note: I am in Southern California in a 'Banana Belt' and have little experience in freezing weather, but our coldest nights so far have gotten down to the high-30's and the plants are all doing fine.
I added a link to the California Rare Fruit grower's banana page - it has notes on frost protection. There are CRFG members in Florida, so the information may be of use to you, too.

Here is a link that might be useful: CRFG banana info page