Excuse me. I made a typo and need to correct what I said.
“If all of your objects are static, then you don’t need to cast any dynamic shadows”
Apologies, you were my first response this morning before my coffee 
What I suggest is try changing the ‘Light Color’ of your ‘Skylight’ to see if that helps brighten the reflections a bit. In other words, you said when you set it to movable it made all your reflections bright. Try keeping it at movable and darkening the light color a bit.