Thanks for writing about your project. I have several friends who play the didgeridoo...
The problem with Arbutus or Madrone wood is that it is hard to find or to process without it cracking as it dries. If you read about the wood on my site, you will see that cracking and bending limits the uses of the wood to mostly smaller projects.
Finding you a piece of wood from an Arbutus tree would not be too hard if you were able to wait a while...probably in the fall sometime. But I could not guarantee that it would not crack as it dries...It probably would. I do not think it would break but it may affect the sound quality. An already dead branch could still have cracks in it, especially as it dries more in the home.
Then there is the shipping question but we could figure that out.