I wear EEE shoes, and I've been wearing Sidi megas (the Genius level) for decades. The mountain shoe equivalent is the Dominator, I think. They are pretty comfortable. Although maybe out of your price range, I've been around long enough to learn that you NEVER skimp on shoes. And cycling shoes last a long time, you'll notice the extra $150 now, but spread that over 20 years or so and it might be worth it (it has been for me).
Of course there's no way to tell if they will work for you, but you can give them a try. I tried Carnac (didn't work for me - didn't feel right) and Northwave (weren't wide enough), never tried Lake.