I have not eaten any Woodchucks but I had an older friend who was raised out in New York state, he told me they used to hunt them to eat. They would string out a can of baked beans for them when they got gunshy. He claimed that a Woodchuck could not resist baked beans from a can. I know they eat them.
I also had an older lady who taught me a good method of cooking Raccoons and I am sure it would work for Woodchucks.
First she said to never try and eat an old one, only the younger ones. Next you have to skin them as soon as you can and gut them, then you take out the scent glands under the front legs, she called them kernels. You then take a knife and cut and scrape off all the fat you can get off the carcass. Then you need to parboil them in vinegar water, this removes more fat residue and gets rid of some of the stronger taste.
Last, you cut up a large onion and an apple, quarter both and stuff them into the body cavity, then do a slow roast in the oven after adding a little liquid to the bottom of the pan. This method turns young raccoons into a delicious meal. I have eaten Beaver fixed this way as well. Cook them long and low to make them good and tender. Bob