Hey for reference here is a picture of some of the meat. I'm new to storing meat in general so I don't know what exactly to look for, maybe it's not spoiled?
That looks like oxygen coming into contact with your meat. It Should be fine. Oxygen reacting with the myoglobin in the muscle cells turns the meat from red to grey. Meat in stores a lot of times is packed in a modified atmosphere packaging, where oxygen is replaced with other gases usually CO2, this is how it keeps the nice red/pink color for so long.
That just looks like the normal color the outside ring turns, it's impossible to eliminate all air contact so the outside edge will get a slight brown color. That burger looks like it will be good for a while longer, most dishes made with burger brown the burger first and after you brown up a pan of that it should all blend together and you'll never tell the outside ring was exposed to oxygen.
If you move your meat around in the freezer, it's easy to nick the plastic bag. That's why so many people wrap in paper over the plastic. It protects the air seal from damage if the plastic gets dinged in the freezer.
The freezer burnt portion will not taste as good Or taste bad. The flavor is distinctive just as is the smell you noted. It just depends on how much you don’t like it. I won’t eat it, but it may be ok in tacos or chili. Vac sealing is better than just bags, but like many here have said having the meat in a true deep freeze is important too ir just eat it faster.
I've been doing this for 15+ years (and back when I used to stack and butcher 6 deer/year). Follow this man's suggestion and call it done. I've even switched to the burger patty sheets from LEM (rather than Saran wrap) to make it much quicker.
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I wrap all my meat in plastic wrap first, getting out all the air that you can. Then wrap in freezer paper, again removing all the air you can. I have eaten meat over two years old and its still good.