As other’s have said, your scene is really faithful to the original, Great Job!
Conveniently for you, Alex Fry gave a talk about the color space rendering pipeline for ‘The Lego Movie’. 
Look at the range of light they were able to use, don’t be afraid to go higher and use the Look, Exposure, and Gamma mapping in the Color Management settings in the Render Properties tab. (Note: I haven’t looked at your file so I don’t know what settings you have used there.)
Now I am not suggesting that you should try to follow it exactly by setting up ACES for Blender using OCIO, but the information is there if you want it. @troy_s has pointed out and detailed the issues that ACES has here and in other posts, so it might lead to more headaches than it would solve. I can’t say for certain.
Good luck!