Talking Dirty (Optical Engineers do this in small groups at OSA1 conventions in foreign cities): Evenly diffuse irradiance patterns made from discrete (separate) points of illumination such as LEDs must be placed in a pattern that fulfils the requirements prescribed by "Sparrows Criterion."
That is fulfilled when they are close enough so their irradiance patterns (light beams) overlap enough to appear diffuse rather than discrete. This typically happens when the centres of the LED light pattern are a tiny bit closer than the point where the intensity drops to 47% of the light cone. The intensity diagram looks like this:
Here's (finally) the hack:
You must either increase the distance between the LEDs and the diffusion screen or push the LEDs closer together until the beams intersect to form a continuous source. (or both)
Find a piece of translucent plexiglass to better diffuse the LEDs light cones.
1. Optical Society of America