Oh no......I'm so sorry, Fred! Crappy luck for the branch to hit your baby like that.
I'm no expert in insurance so maybe someone else can help with that.
The only thought I had is if you had a good relationship with your neighbor *maybe* they would chip in to help defray repair cost. Especially if you are able to leverage the expense down a bit, with your expertise and connections in the biz.
At least no one was injured and your home is OK. And power is restored, I'm guessing.