Anjin,
We went to heavy-duty grinder about a dozen years ago. We used a hand-grinder for a long time, but we basically live on game meat and grinding 100-150 pounds of burger a year got time-consuming. Tried smaller electric grinders, and burned them out within a year or two.
We cook fatless elk (and deer, antelope, etc.) burgers on "open" griddles all the time, and have no problem with parts of them falling through. Just let the downside really brown, instead of simply turning tan.