How about a narrow shelf unit with baskets.

that was going to be my suggestion--a narrow shelf unit with baskets.
There are lots of storage cubes w/ fabric boxes and other pullout stuff that are 12" wide.

There are also 15" ones.
But you could also look for the "drawer" containers/bins, and then have a simple bookcase made to hold them perfectly (bookcases aren't that expensive to have made).


You lose space to the drawer box and drawer slide, so narrow stuff isn't that useful.

One last idea: kitchen cabinets. Base cabinets are normally pretty deep--14"-- but sometimes you can find 15"- or 18"-deep base cabinets that are all drawers.

This one from Ikea is 15" deep.
http://www.ikea.com/ca/en/catalog/products/S19036706/
You'd need to come up with some sort of countertop, but a woodworker might be willing to make one with a routed edge. Either from paintable MDF, or by doing something a little fancier.

If you want to go taller, you could stack them. (I thought Ikea's were boxes without built-in toekicks, but it looks like they stopped making them that way, You could just stack them w/ the toekick, or you could see about cutting the toekick away.


Then there's also the idea of custom. It's worth looking into--it might not be as much as you think. Especially if you're willing to use a premade drawer setup of some sort. And especially if you don't want a fancy finish, etc.
I'd check into this from some kitchen-cabinet maker.

Also, you can't easily do drawers even with your shoulders. You can't see in them!