re; wet .
i dont know if i would go to a backhoe but i would use a sub soiler and go over it good.
but sink it deep as it will go ,this tool will be easy to find or rent . it sounds like the ground is to bound up with silt and this will help it drain. i do this even on high ground to help the ground hold moisture also, it can work both ways. it will help the high ground by holding water in those cracks instead of running over the hill.
i hope this helps you.
take your kids hunting and you wont have to hunt your kids.