I kept copies of the CURRENT files in /tmp/leveldbissue like this:
cd <dir where the leveldb files were reporting missing>
cp -ip CURRENT /tmp/leveldbissue/xxxx-ldb (where xxxx is the deepest dir where the leveldb files were reporting missing)
Each time a corrupted leveldb files were found, do the above and restart the ATS (via Ambari) and iterate until no more xxxxx-ldb/.ldb files reporting 'corruption'.
Here are the files at the end of my iterations through 'corruptions'.
The process was fairly painless though the "recovery" process on ATS restart after removing the CURRENT files did take some time for the busy cluster I was working on at the time. If downtime is more of a concern than preserving the ATS job history, you could consider clearing the ATS data.
Hope this helps - not a nice one to get in the small hours of the morning when you are on your own.