We have used the broomstick method with ducks, cockerels and turkeys no problem. However, we found it very difficult with a tough old goose once, so now use an air rifle for them. One person holds the goose gently over soft ground, whilst another shoots it in the back of the head twice at very close range. We then hang it by its feet and cut the neck so it bleeds out fully.
There are other ways of course, but having done about a dozen geese this way, it's the quickest and most humane method we've found so far.
Eve - how did the hook-on-wall method work exactly?