I am not familiar with your dojo, but it sounds as a good and interesting place to practice Aikido. The study of Shinto and practicing Shinto does in my experience enhance a deeper understanding of Aikido and the teachings of the founder of Aikido. It also brings changes to the body and mind that helps in daily life and in practising Aikido. A sense of deep awe for nature becomes part of that. Just as a feeling of connection with the community. There are not many dojo in the world where one can practice Aikido and Shinto - you are very fortunate!
I don't have much of a frame of reference, but I do think it can help add to an understanding of Aikido...and I do feel fortunate: it's a very rare mix, even more so outside of Japan. It's definately an interesting and beautiful place and I appreciate the atmosphere for helping to instill a certain mindset. I'm a big believer in the impact our surroundings have on our state of mind and I really like the idea of cultivating sacred space for potentially adding to "deeper" interactions/operations. For example, I find the awareness of the centerline running through the jinja has a direct impact on how I pay attention to the centerline running through my own body.
Also, the fact that sanpaisha will occassionally ring the bell and pray at the entrance during keiko, which demands we completely avoid the centerline, adds to the demands for awareness and consideration of our surroundings in general.
...Of course that can be found where ever we put it, not just in a jinja, but that's what I find to be reinforced in what little I understand of Shinto and Aikido.