The darkness of the trench in the movie is mainly due to its depth and the stark top-down lighting; the actual colour of the trench, just like the rest of the Deathstar surface is a neutral light grey.
Your trench is understandably wider than it is deep because of playability (hands need to be able to reach in after all).
So one thing you could do to simulate the stark lighting as done by ILM is to do some zenithal highlighting. You've already painted the trench a very dark grey. So what I would do at this stage is to spray it from below with black to create the deepest shadows. And I mean from directly below the wall pieces.
Then do a light spray of white or very light grey from the top, creating the highlights. Don't overdo either, but bear in mind that the average participant and bystander will mostly view the trench from the top, or from a high angle.
I think this would help you give the trench some dark shadows, while at the same time lightening up your work from where the actual viewing will take place.
Also; when using aerosol cans, make sure to not spray too close to the polystyrene, or the propellant will melt the foam!