Practical approaches to working with nonplanar commutative diagrams?

Question

The 4-associahedron is the 4-dimensional version of Mac Lane's pentagon diagram. If you look at Trimble's notes on tetracategories, you can see the obvious difficulty in working with such a diagram (using it to verify things like coherence etc). Are there any techniques and/or approaches to working with such unwieldy higher-dimensional diagrams?