Have they dried enough yet? If so the dirt might be the problem. I'd use a small excavator with a thumb to pick up the wood and restack adjacent to the existing pile. Shake/ roll any stumps that are full of dirt. You can do they same with a front end loader and grapple but an excavator will be better and quicker. Use plenty of diesel.

Looks like too much dirt and too little density of wood. Consolidate and compact.

The dirt pile in the middle is your problem. Rip the pile apart, restack the wood, and smooth the dirt. It will burn much better.

First thing is to check if your county currently has a burn ban. A lot of the state has one at the moment. Check here. https://tfsfrp.tamu.edu/WILDFIRES/DECBAN.PDF

Basically what my FIL and I suspected. Thanks for the advice all.