Unfortunately I’ve been coping with the same problem for years and have no solution to get the wire chewing to stop. It’s their favorite way of communicating.
It made me decide to NOT share my bedroom with my bunny. If you have the option to move her, I’d urge you to set up the cage in another place in the house. For me, putting Sammy (and Spockie before her – same cage, same chew spots) in the room with the computer and main TV means that I spend my leisure time with her. I even do bills in here and eat because we are company for each other. Either she’s in her cage or out, but basically it’s selecting the room in the home with the most activity going on around her. That relieves boredom and isolation.
You might want to consider a different kind of habitat. You could add an Xpen with a cover next to her cage, with her door opening to it, so she has a wider space to play in. Put a diggy box in there so the morning urge to forage for breakfast is relieved.
Some people try a sheet over the cage at night to prolong sleep, but I’ve not tried that yet. Take care she can’t chew it.