The data directory is independent of any other settings, so in general you can leave as it is the /mnt/data/ directory and make a new directory /mnt/data2/ change path.data: /mnt/data2/ in elasticsearch.yml, and start ES without any data, like a fresh installation but with your older ES specific settings like log path, SSL if you used, etc. Since you have enough the disk space, do not touch the /mnt/data/ directory.
There should be a tool CheckIndex for shards issues. How ES storage works is explained here. There is the topic related to similar issue when an index is corrupted but ES is still up.
I haven't try to copy a single subdirectory from /mnt/data/ to /mnt/data2/ an try to start ES but you have 4 nodes, don't know which num of replica. You can try on a single index. Check index size by command: du -h /mnt/data/ | sort -rh | head -10
Use a smaller size to test which you know that is used with purpose. Maybe is just a bad idea.
Lucene is responsible for writing and maintaining the Lucene index files while Elasticsearch writes metadata related to features on top of Lucene, such as field mappings, index settings and other cluster metadata
The best way is to wait for Christian or other ELK team members to suggest any possible idea in order to save any data.