Thanks for all the great replies!
Sorry for the link dump - I just glanced over the content and it seems like this might help you:
https://www.warpbuild.com/blog/docker-mirror-setup
https://medium.com/@shaikrish27/deploying-a-docker-registry-mirror-as-a-container-59565ff92c48
https://blog.alexellis.io/how-to-configure-multiple-docker-registry-mirrors/