Have you tried using a sacrificial material under your "cardboard" yet? What we like to do for this type of application is use what we call water jet brick and a layer of pink insulation board like you would find at any box store for sacrificial. The waterjet brick helps prevent the jet from rooster tailing off the slats or upwelling and getting your material wet. Generally if you can cut it with a blade you should be able to cut it with water only which would allow you to use a smaller orifice and standoff resulting in less jet flare and kerf width. Oh and just a quick description of water jet brick in case you are unfamiliar with it, it is corrugated plastic blocks with an approximate dimension of 6"x4"x4'. you can get quite a bit of life out of them be for you cut them up to the point that they are unservicable. For cost effectiveness it my be best for you to use it given that it will drastically reduce bad cuts due to excessive moisture absorption. Hope this helps!