Apparently they do not eat the cob

I've trapped areas of alfalfa that had perfect half circles cut.

cool. do they eat it or just build dam, or both, have any pic of dam??

Here it seems the only way to trap them is under a nuisance permit.
They work the corn and beans up till harvest, then leave the area.
Sometimes they're not far away on the river, and a scent post or mud pie set will take them during season.
Harvest is normally long before season opens here.
Plus being on a river, you might trap them all, and a week later new one or two show up.
Here you can set almost anywhere on a river with a mud pie set and catch a few.
Usually two year olds kicked out on their own.
Breeding season they're running the river a lot.