So I obviously needed to figure out what I was building before I built it. This was surprisingly difficult because the vast majority of the information presently on the internet is in Japanese. Baumkuchen is a very popular pastry in Japan and as far as I tell can only be found in Japanese markets in the United States.
The first place to check is Wikipedia! I don't know what to say about Wikipedia except that reading it first is the best introduction to the cake.
The closest things I could find to cake oven plans were this video and this video. They display how the batter is applied and shows the rotors spinning at about 40 rpm.
I also found two recipes: a Japanese one here and a simpler German one here. I can't read the first link, but I've made the second one as a delicious flatkuchen (which will be explained in a later post as well).
I also did hunt for professionally-made baumkuchen ovens for inspiration. Again, I was handicapped by my being monolingual. A friend helped me contact several Japanese companies to ask for price quotes. Koyo Machinery Co. sells a behemoth that apparently makes 12 baumkuchens at a time, but they would not respond to my e-mails. Fuji Syokai has what I think is the best oven for noncommercial use, but they are rather enigmatic; I could not locate a website or even an e-mail address. I sent them a fax request for a price quote and received nothing back. At the very bottom of its catalogue page, oven.jp shows two of the three oven models they sell. The one not displayed, UA-431, is presently out of stock. They would not give me any information on MA-111. UA-343 is 680,000 JPY before shipping costs.
Edit: Oh man, I just noticed that UA-343 is, in fact, manufactured by the mysterious Fuji Syokai and sold by oven.jp. Sweet!
After that, I started designing ovens. But first I had to make my own flatkuchen.