Going one step further with Sunshine0063's suggestion, what if you bake your three tiers of cake, but make them 4 inches smaller than normal. Then bake a larger tier and using a ring mold, or a clean can with both ends removed to cut out your cylinders. Then cover them with fondant and attach them to the outside of each tier. This is all assuming you want cake for the whole thing, rather than say, RKT or even cardboard tubes like what is often used for castle cakes. I agree, it will probably be a pain, but I think it's doable. Oh, and your cake boards under the tiers would be large enough for the "diapers" to sit on.
Your cylinders for the diapers shouldn't be any more than 2" in diameter, probably smaller if you can do it. I'm thinking a Red Bull can might be the right size. I've made real diaper cakes, and the rolled up diaper, depending on the size is smaller than 2" diameter.