The degus main characteristic is chewing and I know of a lot of people who have gone crazy about it.
Guess there is not much you can do but provide them with more and intering chewing objects in the cage. Mine rather chew on branches (safe are apple tree, hazelnut, birch, willow, all not sprayed of course). Mine also chew more when I donīt have a wheel for them. Oh, please always provide them with lots of Timothy hay, they also love to chew that and it should be their main part of their diet.
Yours wouldnīt be the first ones who chewed through the plastic cage bottom. You could put tiles on the floor and protect the corners with metal shields (home depot) or build a new base of sheet metal or tiled wood.
I wouldnīt be worried about waking them at night, theyīll find time to sleep when they want to. I found outthat they are pretty active at night anyway. Iīd be more worried about getting enough sleep myself. Canīt you leave the cage in the living room where you donīt here them at night?
As for the taming - patience! I wouldnīt force them and offer treats on my hands so that they think your hands are a great place to be. Mine started climbing on my arms and shoulders but
still feel uneasy being transported on the hands but a few and I canīmove to another shelf inside the cage without jumping off.
When one escapes, I recommend having a box with a hole and letting them hop in and then cover the entrance, or use the sand bath if it is in a glass bowl, or a cardbox carpet roll and cover the openings up with cdīs. They usually like to explore dark caves and it is easier than chasing them around.
Hope I could help.
P.S. I throw the food on the bottomof the cage and put hay on top of it. They are busy trying to find the food and Ithinkit gives themsomething to do. In the wild they need to work for their food as well.... and itis funto watch them