We don't have Elk, we have Whitetail. I find it easier to grind Boston Butt with the Whitetail, instead of trying other things, also it makes a biger pile of meat from a small deer. I don't usually make burgers with deer, preferring beef. I use it for chili, soup, etc. I vacuum-pack it to avoid freezer burn.

RyanF- I live in Alabama and put the meat ( except the liver) in a clean trash plastic trash can (used only for meat) covered with salted water ( I know, "Horror Horror"). This helps take the blood out and is cool enough in the winter to keep the meat a few days if the water is changed every day. I have been married to the same woman over 55 years, partly because I took her clean looking, sweet, smelling meat, without a lot of blood. When it starts to smell or taste "gamey" the cause is usually blood. I know this is counter to accepted practice, but it works for us.
Mike