It is a complex problem but it’s one worth solving. Just spit balling but I think you could reduce some of the difficulty maintaining it by shifting it away from ops to development. Keep the disaster recovery level database backups for that rainy day but make customer level backup/restores an integrated feature developed and maintained like other services.
I wouldn't be surprised if a lot of the time was spent just waiting on the ops team to perform restores. If it's a manual/labor intense process, it's likely take them a while to work through the entire list
