I have another idea. Could you randomly -- and by randomly, I mean assign digits 1 through n to the different versions of the track -- string together 15-second cuts of different tracks so that you're left with a seamless track that smoothly transitions between bit-rates?

The overall goal would be for the listener to identify which 15 second spans are encoded with the highest quality, starting at time index 0:00, 0:15, 0:30, etc. Since you'd assign the parts randomly, you may end up with a few consecutive spans of the same quality. With the chunks only being 15 seconds long, you'd also increase your chances of using all the bit-rates before the end of the track.
I can explain it to you but I can't understand it for you.