Some more ambient lighting can help. I’m not sure how you would have ambient lighting in a cave, but think of something. Maybe there’s a bio-luminescent plant or animal species living there, and it’s bright enough to provide soft, natural light. Maybe the cave isn’t too far underground and there’s some natural moonlighting filtering in. Maybe there’s a crack in the floor and a lava river underneath, spewing smoke through the crack and lighting the cave that way. If this is a modern cave, you can have work lights and cables running along the walls to light up the environment. If it’s an old cave, torches, oil lamps, anything to get some stronger ambient light in here.
It seems you tried the moonlight solution, but there should be a much stronger light/shadow being cast than what I’m seeing now. Don’t be afraid to add static lights in order to fill the room.