I did this project in Ableton Live. First, I imported all the stems. I let Ableton warp the stems without any intervention on my part. I then created four tracks, drums, bass, piano, and lead. These would more accurately be called rhythm, bass, harmony, and melody. I put each stem in whichever track I thought best described it. Some stems were rhythmic, and others melodic, but it was hard to categorize others. So some of my classifications were somewhat arbitrary. Also, I made sure each track had roughly the same number of measures by moving some clips from one track to another. This moving about of clips added a bit more arbitrariness to the categorization.
I converted each clip into a loop of length 2^n where n was the largest number so that 2^n was less than or equal to the number of measures Live had warped the clip to.
I then used follow actions to trigger the progression of clips downward through each track. With a probability of 1/3, each clip would repeat, and with a probability of 2/3 would go down to the next clip. Then I started the first row of clips and let them go.
In the final mix, I let the last loop in each track continue to its end, rather than ending abruptly in the middle.
I added a little echo and reverb but did not alter any track (other than the warping done by Ableton). I used every track and did not add anything of my own.
If I had to use all of the tracks, as I did, I think I had to come up with a mechanical, deterministic process like the one I used. Otherwise, the choices I would have to make would be overwhelming.