Whelp, guess what I forgot to do this entire time!
After I changed the directory permissions to elasticsearch, I did get the following:
[root@3107e4c11987 /]# curl -XPUT -H "content-type:application/json" 'http://localhost:9200/_snapshot/snapshot' -d '{"type":"fs","settings":{"location":"/backup","compress":true}}'
{"acknowledged":true}
I was then able to delete pre-existing indices, restore, restart, and bring up graylog with all my data. Glad to know that I'm ready to migrate my server over.