Finally figured out what it was and stopped it!!
Everyone is probably tired of my ongoing battle with the mysterious night marauder, but I've finally got it clear. After many nights lying in bed and hearing something dabbling in the creek right under my bedroom window and putting that together with the torn up paths, it got through to me that it must be a coon.
So I got someone to move my single strand electric wire down to about 6 inches above the ground and baited it with cotton balls soaked in salmon juice and wrapped up in tin foil. That night I heard it cross the creek, and then quite soon return. It still comes into my yard and tears up the mulch in the ornamental beds but it hasn't climbed the fence around the vegetable garden.
I just hope it has a good memory of that shock. The corn is coming on.