In your area, you would probably need to plant at least 6 inches deep.
NO, NO, NO! 6 inches will assure that they are buried rather than planted! No garlic, elephant or otherwise, needs more than 2" of soil above the tip of the clove. That's an inch more than recommended by most professional growers. Some even advise just barely covering the tip. In our 5,000 plant field, elephant garlic and regular garlic are treated alike as far as depth of planting goes.
Mulching is not going to prevent frost from going deep into the ground in our cold zones. Instead, it prevents or deters freeze-thaw-freeze-thaw cycles which tear the roots off of bulbs and tubers. We use 3" of oat straw in the field and 2" of shredded leaves at home.