I'd go crazy if I had to cut my deer in small enough pieces to run through our Kitchen Aid grinder. I have an old grocery store grinder, so not much help there. I do use a vac packer, but only for steaks. Do yourself a favor and get one of the Cabela's or similar commercial grade sealers. I went through 4-5 Foodsavers before buying the Cabela's about 15 years ago.
The best way to pack burger is with a vertical sausage stuffer and the poly bags from LEM. You can buy 1000 bags for about $40. I can package 20# of burger in about 5 minutes, airtight, no freezer burn and lasts for years. I've lost several bags of burger in the freezer to find them years later, and they are still good.