There are a lot of good suggestions in this thread, but frankly, I've stopped reading them because I don't think Blizzard is likely to do them. I don't think they're paying attention to our ideas, and even if they did, I'm starting to suspect that their abilities to manipulate the game's code for these brawls are crude and somewhat minimal, so complex changes like arena mode or swapping decks are way too complicated for them to implement. Maybe the initial introduction of TB was just a starting point and they'll add changes to allow more ambitious brawls in later patches, but I'll believe it when I see it.
So, in the datamining on the last patch, there were several other chalkboard pictures similar to the one for Rag vs Nef. Do these other pictures relate to the next few brawls? If so, any idea what they might mean?