Dig them up just before a frost. They don't take kindly to that. You should have an idea when your first frost comes. I dig mine up and lay them down on the garage floor, and let the good go back into the bulbs. Then they are cut from the step, powdered in fungicide, and stored in paper bags with labels. These bags I put into a cardboard box and then are stored in the cold cellar for the winter. A non freezing garage will also work. I've been doing this for years, and it seems to work out well.

You have a lot of cutting to do, so you may not have all the room that you need. I've also seen folk bend the tops back in half after the flowering, and that forces the nutrition to go to the bulb as well. That might save you "the garage" step as room may be a determining factor.