I cooked woodcock this afternoon in the traditional method in accordance with Scott Rea's video instructions posted by the OP above.

It's labor intensive and produces good results. I believe alternative methods such as described by others above are fine as well. A word about the traditional method: guts are left inside. It sounds rough, but consider this: Ever smell the insides of a gutted quail? Pretty bad regardless of how fresh. Woodcock have no smell when gutted. Maybe it's because nothing stays in the intestines for any length of time. Anyhow, the only complaint I had was the gravy was gritty. The gizard is not utilized, but perhaps sand is passed through the digestive tract and that's where I picked it up. The brain? Okay, not anything to write further about. The flavor of the meat was very good and the gravy not overpowering. I may do it again in the future, but I've done it once and don't see the immediate need to do it again.