I don't think that freezer burn actually ruins things (?) unless the freezer burn goes all the way through an item. I may be wrong but that's my impression. I think the deal about freezer burn is that it changes the texture of things. Also, some things will acquire a freezer flavor if you keep them too long, especially in the smaller over-the-frig freezer that cycles on and off often.
I don't have any experience with frozen breast milk, but you got plenty of feedback on that aspect.
I occasionally have meat or frozen vegetables get freezer burned if I lose track of some item. The vegetables are usually a lost cost :) because the pieces are so small you can't cut off the burned part to salvage the item (ex: corn). But with frozen meat you can let it thaw slightly and shave the freezer burn right off and the meat tastes fine.
You can also "see" the affected freezer burned part so you can tell what to cut off.
I think the aspect you want to be concerned with is the age/efficacy of the breast milk. If you want to do an experiment to see if freezer burn looks different, you could probably excellerate the burn process by taking a package of your milk, taking it out of the bag and putting it in the small freezer in a bowl or a paper bag so it will be exposed to air and putting it back in the freezer, preferably the smaller freezer in the top of the refrigerator. After a while you will be able to see the drying out/ burning process.
Have fun
Oh, another thought: seal-a-mealing after the milk was already frozen may not be as ineffective as you think. The goal is to keep air/oxygen from getting to the item. The double layer of plastic would help with that. So would white freezer paper/alum foil/heavy duty freezer bags, etc.
PS
I decided to come back and add a post script because I wasn't sure if I had made myself clear. You see, there are two separate issues here: one is freezer burn and one is spoilage. Something can be spoiled without being freezer burned and vice versa.
The freezer burned area is simply dehydrated - that is what freezer burn is. That's why we wrap stuff - to keep the air out to keep it from drying out and getting freezer burned. Food will stay good longer if it doesn't dry out because that can change the texture and the exposure to the freezer air can also change the flavor. But those two changes don't mean that the food is BAD, as in SPOILED. The food is still edible, just not palatable.
Spoilage, on the other hand, is when something becomes poisonous or bad for you! Yes, freezer burn does "spoil" the palatability of the food, but that is based on taste/likes and dislikes. True spoilage usually takes place either before or after (as in the thawing out process) an item is frozen. Much of the time spoilage can be smelled or tasted. Sometimes it can't be and that's when people suffer from "food poisoning."
It may be that if your milk is freezer burned, you might be able to cut or shave off the part that got dried out without it affecting the flavor of the rest of the milk. Simply do it before it thaws out. If your milk did not sit around on the counter too long before you froze it and the freezer did not go through a power outage, then your milk is probably still good unless it is too old. The taste test will let you know if it's still good.
Sorry - the teacher part of me came out!
Hope this helps!