I know exactly what you are saying and have struggled with the same problem. I recently had a longish motor trip with a friend who though not overly religious is a believer. I talked about my relationship with the natural world as an amateur naturalist. The conversation got fairly "deep" and the word she used was spiritual. I immediately bristled at the use of that word but, could not come up with another way of describing my feelings or reactions. There is nothing spooky about how I feel in these and other situations. It is totally internal and personal. Once an acquaintance I was walking with at sunrise mentioned how god had put the sunrise in place just for us to look at. I told him that I'm not a believer so why would this god of yours want to entertain me. I still felt the awe and beauty of the moment but, I didn't feel like praising anyone except the random sunlight squeezing between gaps in the clouds and reflecting off ice crystals and water droplets in the air. No miracles involved. Just an event that happens because it does. Knowing what is really happens and the science behind it makes me feel good. Reality is so much more satisfying than "spirituality". I haven't answered your query because I don't possess an answer. Not in one work anyway.
Russ.