Your observations are very helpful. Intersecting light sources are often a problem. That’s why I suggested to bake all static (= non-moving) lights. This way, the lights would not exist in your final scene anymore. Instead, the light becomes part of the texture as though you painted it on the blocks. The moving light source of the ship would interact with the texture only, not with another light source.
Make the all non-moving objects static in the Inspector. And set all non-moving light sources to static as well. Then go to Window > Rendering > Lighting and click on “Generate lighting”. The scene should look exactly as before. Then test your game.
If the issue persists, you could go to Edit > Settings > Quality and check if you can tweak some values or enable something. Since WebGL is a “weak” platform, try to aim for the lowest values with which your game still looks good. The lower, the better.
Then test your game again. It might be that some effects simply occur because the browser has so much to do.
See also: