Sheet mulching in North Carolina?

[OneGrassRoot]

We can't grow grass in half of our backyard due to large tree canopies, and no shade-tolerant seeds have worked. So, I'd like to come up with an inexpensive alternative that will prevent the constant mud.

I just saw a video about sheet mulching where they lay down a layer of cardboard and put wood chip mulch over it. It was for California, however; not sure if the climate matters? The humidity and rainy times here does make me worry about mold and such. I did a layer of hay one year as a quick way to cover the mud and that was a mess...lol.

I know people do sheet mulch with the intention of planting in that area eventually but I'm really just looking for something that can cover the mud, help stop erosion (the yard has a slight slope) and the area can be used for children to play on.

Thanks!