Sam's Club sells commercial entry mats. We figured, if they work to keep humans from tracking things in, should work for cats. You may not have enough room to unfurl one, though. Not as cheap as the Ikea example, but under $30, and like people have said--shake them out. These are ridged, but they are soft, so our cats did walk on them.
Bonus: they are rubber backed, so if your cats go through a spraying / peeing period, they are impermeable.
In Ireland, with nowhere near the room, we switched from clumping to crystals. They do still track somewhat, but it is greatly reduced, and it is greatly reduced odor, particularly immediately after use.