I've never had to share a fridge before with other's stuff in there.. Maybe you could get a large covered container, and break the meat apart into chunks, place them in the container, and take off the lid to get air twice a day, and ideally turning the chunks over each time.
Personally, I find ground beef a little hard to eat, as in, I don't care for the taste without having to disguise it with salt, pepper, etc. thus I buy the cheaper roasts and thinly slice with a very sharp knife.