Moises - This is a provocative query and offers a wide range of inspiring possibilities for a composer. Before I start to offer my answer, I must say that your final questions, "How would you as a composer interpret Cubism as a musical form? What would it sound like?" are your best answers. In other words, I think you can best answer this with your own music...and I believe it could be a wonderfully inspiring challenge.
Susanne K Langer, a renowned philosopher of aesthetics, has said that art is the expression of a feeling that cannot be described as well with words. There are no rules in art except for the ones artists choose to impose on themselves. Many have used mathematical and scientific principles as inspirations for a work but the way the use them is completely subjective. Their use is metaphorical rather than literal. The principles of cubism you describe above are visual principles. You can choose any of the terms therein and make your own translation into music terms but that translation is metaphorical, not literal...it is subjective and for that reason specifically, it is a creative act. Composers who have used Schoenberg's 12 tone system, which had rigorous mathematical rules, found the need to get very subjective about its use in order to make music that has any value.
Your thought about a fugue as musical cubism is a thoughtful comparison and, for creative purposes, could be useful for your musical answer. However, here's another wrinkle. People react to music emotionally. I would react emotionally quite differently to a Bach fugue than I would to a Braque painting. Now, if the fugue was by Stravinsky or Bartok, the feeling evoked might be more similar...but that would not be because of the structure as much as the musical materials (harmonic and melodic) style which would be more contemporary with Braque and therefore coming from more related creative place.
When I was developing myself creatively, I used to go the an art gallery, stand in front of a painting that fascinated me and think about how to translate what I was feeling into music. So, I think the question you pose is a valid way to stimulate your creativity - a good one. I would simply suggest that instead of looking for literal rules, mathematical or structural exactitudes, you treat your query as an inspirational gift pushing you to find your answer in your own composition. Using any of the descriptive terms about cubism is a valid jumping off place. By the way, I agree that cubism and its practitioners you mention above are fascinating.
Thank you for a stimulating question,