In a sense, what you're doing now is staring directly into a light source. It's really extreme, and it's attention-grabbing, but there are a lot of other aesthetic options for a project like this. The lights could be illuminating an object, or they could be casting shadows, or they could be projecting a pattern onto a surface.
This is a great time to experiment with different materials, to get a sense for what the LED light looks like under different conditions. Maybe this will give you ideas about other materials you'd like to try, or other visual effects you want to design.
First, a simple piece of printer paper. I folded each edge down into a sort of box-lid shape, so that it's separated from the LEDs by a fraction of an inch. This gap gives the light some distance to spread out before it hits the paper.
Next, let's take the same piece of paper, crumple it up, then flatten it. This adds a lot of interesting texture, and you can start to see how the moving light interacts with a complex 3D object.