Really nice results!
I am very fond of this method myself, and have used it with a lot of success elsewhere. I'm planning to do some lasagna-ing this fall for planting in the spring.
One thing I learned (the hard way) is that it is much easier to work with the cardboard if you wet it first rather than lay it down and then try to saturate it with a hose. Fill a big container such as a horse trough if you're lucky enough to have one of those, or a deep wheelbarrow, a (clean) garbage can, or one of those big tubtrugs, and soak the cardboard pieces in the water until they're saturated, before laying them down on the ground.
