The information on what the container is currently doing is stored in the CurrentOperation field of the build context. A couple things to remember though:
1) This field is of type object - unless you go through everywhere that sets this property and finds the type, pretty much all you can do on it is call ToString on it.
2) The entire tree is not stored, only the current path the container is working on. Once a dependency is done, the information in CurrentOperation is overwritten.
So you'll need to add a strategy at the front of the build chain to collect this information and assemble it. So there's still some work on your part to get this.