I will suggest to create a list of permabanned user for copy/pasting and moderators giving track that which post of that thread they have processed. This will help in reporting as we can easily check whether user is already banned or reported by other but pending review by moderator so no need to take action or re-report.
A Rank "Banned" has been suggested before (by me and other people). That would be the fastest way to know an account is banned already, and doesn't need further attention.
but it does not look to me that moderator has gone through the whole list
I'd go through the whole thread myself to list them all, if there would be any way for me to see if an account has been banned already. But I can't see that, so I can't easily make a list of accounts that still need to be banned for plagiarism.
Report to mod is for reporting anything.
Chances are the Mod who handles the ticket can't ban the user. Most Mods can only nuke Newbies. The post will get deleted, but the user won't get banned.