I like the Artbin products best. Rather than the Semi, I'd go with the Super Satchel. You'd be able to have 4 stacks of charms per bin. They come in depths of 2, 3.5 or 6 inches.
I've had the ones like Faintly Artistic and liked them, but the tabs that lock them together or snap the top on, depending on the style, have broken over the years. I had a set that was 2 deep and one that was 3 deep.