The University of Georgia does research on cold hardy bananas at a facility nearby and a researcher told me to never discard any banana leaves you are removing but to mulch the plant with them. You can either just lay them on the ground whole or cut them up and work them into the soil but always use that free fertilizer, it is an excellent source of potassium. When I cut back my trunks, after the foliage has browned off in the winter I always slice up the trunk and lay the slices (this is a VERY MESSY job) on the ground around the base.
David, since you are digging your bananas, I would just incorporate any waste into the soil where you intend to replant the bananas next spring. The plant tissue should be well broken down by then.
Also, remember to take a soil sample and have it analyzed so you know how much additional potassium you need to add. While M. Basjoo's are unusually hardy, you are growing it outside it's normal range and soil conditions may be very different in your area.