You're on the right track.
The reinstall step of the newer CentOS version will completely overwrite your system which is why step 0 is very important. I would strongly suggest that in step 0: grab all backups from /var/airwave-backup as a precaution.
Once reinstall is complete, restore your backed up date. Once the backup is restored, make sure to check the UI to make sure the data looks consistent with how it was before.
The general rule is that you can skip 1 release in the upgrades or you can play it safe and go through each of the upgrades (7.6 -> 7.7 -> 8.0 -> 8.2). If you want to skip, you should be able to go from 7.6 -> 8.0 -> 8.2.
At that point, I'd have to run through the upgrade path again to be certain, but I think it'd still show as CentOS 6.2, but a fresh 8.2 install will have CentOS 6.6. So depending on what the cat /etc/redhat-release value is after the 8.2 upgrade, you may or may not want to repeat step 0, and then reinstall / restore once more so that you're up to date from all angles.
Another thing since you're upgrading from 2 year old code is to double check that your box is still up to spec. Several new features have been added that gobble up resources.