I'm so glad everyone has been helped by my post. I don't post often, so it's good to know it's worthwhile!
I just made another trip to Ikea today and discovered some nice cabinets in their bathroom fixture section: The Silveran, The Lillangen, and the Tyngen series. The cabinets are not too deep, not too wide, and look like they'd be great for fat quarters or similar. Now I just need a place they would fit! Perhaps I could start hanging my fabric storage containers from the ceiling, LOL!