Ceanothus suffering bad winter damage

I'm hoping someone might be able to help me. We have a rather nice Ceanothus which we inherited with our house and unfortunately the last two winters have hit it really hard. Most of its branches are dead and covered in a green growth. There is some new growth on it but it is sparse and doesn't appear to be particularly strong.

What should I do with it? I'm tempted to cut back all the dead branches but it will then look slightly strange as it will just be a tall thick trunk with some sparse green leaves at the top! I'm reluctant to cut it down as I love the colour of it when it blooms. A picture of it in its current state is below.