You can help dry out the top of the soil with a bit of air flow across the top from a gentle fan. That doesn't help the soil compaction of the rest, but you know what does in an organic grow?
That's right,
@NickHardy 's worm castings. They're covered in a calcium carbonate slime when they exit the south end of a worm moving north and, according to
@Gee64 , the calcium helps open up the soil by turning some soil particles on edge adding to the air exchange.
There seems no limit to the simple worm casting. "Now available at retailers near you!"