How to prevent moisture in my firewood?

You are precisely correct: the tarps don't allow the moisture to escape. Humidity cannot be managed - rain can. If your wood is outside, just cover the top of the stacks and let the rain and wind, etc. in from the sides. If you dried the wood over the summer (and if it is indeed dry), you can leave it in the rain and once you bring it inside by the stove, the moisture will be gone in one or two days. But best method is cover the top, let the air circulate from the sides, and you'll be good to go.