Welcome to BB!
First off, thank you for taking them in from a potentially dangerous situation! Who knows what would have become of them if you hadn’t stepped in!
Just from what you’ve said, it does sound as if lack of space may be an issue. If the cage isn’t large enough for them to “get away” from each other, this can trigger territorial fights. Each rabbit requires a minimum of 2×4 feet of floor space (not counting vertical levels). So if the cage or pen for each pair is smaller than 4×4 feet, it is too small.
The other issue is that they are not fixed. Hormonal behavior can make it very difficult (impossible?) for two rabbits to safely live together. You’ll hear the occasional account of two same sex, intact rabbits living together long-term, but this is very rare.
What is your goal with these rabbits? Do you want to keep them all permanently, or are you selling new homes for a couple of them? Can you spay/neuter them one or two at a time over the next few months?