That tarp should help a little. That just looks like a moist area, and not much airflow. Looks like that outer, lower corner may stay damp, but the rest should be ok. When you deplete that pile, stack it a little further off the house, like 6" of airspace. It's not anything you're doing wrong, just kind of a challenging spot. In this case, do everything you can to keep any residual water away and try to have lots of airspace.
LOL... nope. Just right next to a creek, in a ravine, and well covered with tall trees I was hoping it might be just a challenging spot and not the overall setup.
I'd say that after seeing your set up you are dealing with a less than ideal situation no matter if you cover it, how you cover it or what you use to cover it with. The moss growing on your shingles tells me that. Its to bad you don't have a place to park yer wood out in the sun and some breeze during the warmer months to get good and dried out and then get it under cover. My stacks are left uncovered all year until around till Oct. then I cover what I think I will need for the winter. But then I'm here and your there so your mileage may vary.