I keep coming back to wool also. You state you have moths. In my experience, moths have only destroyed items that were being stored, not items that were actually being used and washed on a regular basis.
I have never heard of anyone sneezing because of cotton batting.
If you want "environmentally friendly", avoid bamboo. They claim it's sustainable, but the process it goes through to become soft batting is horrible for the environment.
My favorite batting is Quilter's Dream, both cotton and wool. I used wool in the quilt that lives on my bed and it deserves the name "dream". I wash it in cool water and tumble dry low.
Another thing to realize with wool batting is it will be completely enclosed by the top, backing, and binding.