I would recommend shelf risers, so you could divide those cubbies into more total shelves to hold the shoes. Get stackable ones, and you could do 2 or 3 levels on the long upper shelves, and on the bottom tall cubby. Or if your budget is large, you could get the shoe boxes at the Container Store that have a drop down lid, so the shoes can be pulled out of the front of the box. You could stack those as well to maximize storage per shelf.

Elfa drawers are great for making a customized dresser in a closet, where you don't need it to look like finished furniture.