If you want to go vertical, consider bells. Also, heat rises, so its much easier to heat the second floor.
Our designs utilize clay chimney flue liners rather than cob because we are using bells and chimney flue liners are designed to support their own weight. In order to create a cob shape of the same height, you would have to create an very large pile at the base. Clay chimney flue liners can't handle temperature changes greater than 50° per hour, so they have to be insulated by ceramic fiber blanket, dense fireclay bricks, or an inside layer of smaller flue liners.
If I build the battery of bricks and cob on one side of it, would the wall itself function as a thermal battery to radiate in the other room?
Of what is the wall made? Standard frame construction does not a good thermal battery make.
The blog in my signature has an article explaining the difference between bells & flues.