The cardboard + mulch sounds like a winner. Or even a thick layer of newspaper under the mulch. Have you tried pine straw? A nice thick layer that stops 2" or 3" from the base of the plant works better than any other mulch I have tried. When I had my landscaping business I tried them all. The straw packs down and the needles twine together makeing an excellent weed block while still allowing water to get through. It also decomposes very slowly. Much slower than wood mulches. I also find it very attractive - very natural looking. The next best for weed control is shredded cypress bark mulch. Do be careful not to pack the mulch up against the base of your plants.
Even without the cardboard or newspaper the pine straw is great at weed control.
Elizabeth - or Your Majesty
Living and growing in Lafayette, La.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant. ~Author Unknown