For mats, after vacuuming, I wet them with the hose first, then spray or pour (if the staining is REALLY bad) my 1:10 Castrol APC solution onto the stained areas. Then I bust out my stiff nylon brush and scrub till the stain goes away. Hose it down with water and scrub some more if necessary (recent bad weather = really dirty floormats). Keep shooting it down until the suds go away, then extract with the Little Green (which I think has less pulling power than your Ridgid). Whatever flat attachment you have should work fine.