Don´t worry. The fight with lots of noise aren´t the bad ones. As long as nobody gets hurt (even ripped ears, little wounds are still okay), they are fine. They probably need to sort out who the boss is. I wouldn´t let them out of the cage though before the issue is solved. Smell is very important for them and if they are in an "unknown" area which is not marked like their home is, they can feel threatened in their position and will want to reestablish the hierarchy.
Same thing when you clean the cage. Make sure that you sprinkle some of the old litter over the new, it definitely makes them fight less.
In a group of two there shouldn´t be constant quarrelling once they have sorted it out.
I have no clue what the measurements of a 60 gal. tank are but to give them more room, you could add a wire cage
on top because they really like to climb. You´ll find an example on www.degus.org
A running wheel (at 11-12 in. in diameter and tailsafe) will also help to redirect energy.
Good luck, I´m sure they´ll be fine, it didn´t sound critical what you wrote. But watch them closely and make sure that nobody is too afraid too eat and that they still act normal. As long as they still talk to each other or cuddle once in a while, things will be fine.