@phildawson I am not using an LED or laser projector and I can’t answer you directly.
Does “fairly well-lit” include direct or indirect sunlight? Sunlight may (as @robbo says) cause Kinect problems rather than projection issues. The Kinect is an infrared camera, so IR sources may drown out the Kinect light source.
To possibly avoid both visible and IR brightness, can you instead add a shade over the sandbox so that it is in a dimmer area?
For our outdoor sandbox use, I set up a canopy around the sandbox.