I have written to them. They wrote back telling me to use the data matrix to answer these questions. https://tcga-data.nci.nih.gov. After downloading it, I was astonished to see the amount of data missing. It looks like the kind of exploration we intended is not possible--or at least not easy--using TCGA.
On the plus side, their data matrix does appear quite useful. It would just be nice if they could relax their iron-clad grip on level 1/2 data to make it a little less annoying for researchers to get to.