You don't avoid speaking. You do nothing that indicates you are mad, cold, sullen, etc.
What you do avoid is initiating other means of contact throughout the day. Don't text or email, and don't call her. If she initiates, then respond. When yomelet home, speak to her. But let her initiate conversation. Let her lead, and you learn to listen (eyes on her as she talks) and validate when you can. Don't follow her around and talk to her. Be nice, but don't overkill, like most LBH'S want to do.
This is one of the ways you give her space and don't smother her emotionally.
I think it is real important you not try to fix her. Seriously! She doesn't want you trying to fix her.
If you will step back and let her breathe, it will do more about those walls than you may think. Stop thinking of what you can do to help her and focus on what you need to improve about yourself.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!