If you are handy, I'd look into motorizing a classic cast iron (or stainless version) grinder. Most are designs that have been made for decades, and the parts are kind of universal. The #32 size would be a nice overkill for your needs. Something like this (or the cast iron version is much cheaper).
Nella #32 Stainless Steel Manual Meat Grinder is available at Nella Cutlery for the Best Price in Canada. Shop Online or In-Store. We serve all across Canada.
nellacutlery.ca
I have a #22 size that runs off a 3/4 HP motor. It has a V-belt drive into a gear reduction and it makes quick work of 30 lbs batches of sausage, including fat that is a bit too frozen still. It would be sufficient for your needs I am sure, but I wouldn't want anything less, especially for products that aren't so well suited to continuous duty. Realistically people don't process 50 lbs a minute. Even with helpers, you won't grinding 500 lbs of meat from your hunting party in 10 minutes.
I think many people build them simpler, with just a V-belt and 2 pulleys to slow it down enough, but having the gear reducer is really sweet. I didn't build this one, but I have thought of rebuilding it and improving some details (notice I use a shim it to make the belt tight haha)