If the story isn't to follow the tradition narrative structure of the story, then the animation at least has to be presented in a way which relays key information of the story. I think I'm thinking along the lines of something like Bunuel's Un Chien Andalou, Robert Altman's Short Cuts or even J.G Ballard's The Atrocity Exhibition. William Burrough's Naked Lunch or Ryu Murakami's Almost Transparent Blue. Narrative which feels superficially very loose but underlying themes bring it together.
It's a method which gives me the room to remove a lot of exposition and giving the animation an episodic structure without a desire to tell the story in full. Which also gives me a few ideas of how to incorporate the best parts of the voiceover into the story without an over-reliance on text. For example it could be broken down into these chunks.
1. The games of chess
2. Sargent Major Morris
3. The wish
4. Herbert's death
...and so on. This gives me a definitive running time for each vignette and a clear theme to focus on for each. The next step will be to pick out these bits of text.