John, if this slab is at grade level and getting wet, doesn't this also mean your siding is sitting in the dirt and water? If there were anything I could do to adjust the exterior grade to provide better drainage, and clearance from the siding, I'd do so.
If there is no external room for correction, you could use brick pavers to gain the 1" needed inside. Pavers are available 1" thick, and could be mortared in or loose laid, but you still need to find a way to keep the water from reaching the floorplate of your studwalls. By chance does your laundry have a raised concrete stemwall, higher than the floor except at doorways? If it does, then you would not need to raise the entire floor, but just do a concrete curb at the doorway.