Individual site backups & staging

I am working on a large multisite network, and we are currently only able to have full network backups. We are also only able to push the entire network from staging to production and vice versa. As you can imagine this is fairly ineffective for us. If something goes wrong on a site we only have the option of restoring the entire network, which takes hours and erases all the work someone may have been doing on the other sites. We also can’t use our staging environment effectively because we are constantly working on at least a handful of sites over there and pushing one way or the other would also overwrite changes. I’m wondering if anyone has had any experience doing backups, or effectively using a staging environment on a site by site basis? Or some plugins that have this sort of functionality, though I have yet to see something do anything like this. I’m more than willing to write a custom solution, just thought I would see if someone has done something similar in the past so I’m not reinventing the wheel.