There's another solution, which is to require all appeals to be done via e-mail and not in a Meta thread. The threads seem to be useless anyway; I think I've seen only one of them in the past few months where a person was erroneously banned, and it got reversed--and I'm sure that could have gotten resolved via e-mail.
The threads might help to take the load off admins/moderators because often these questions can be answered by regular users e.g. by showing plagiarism examples. Unfortunately some recent shitposters have been quite belligerent even after being presented with solid proof so the threads rage on for multiple pages where 2 posts should be the end of it. Also I'm seriously doubting the sincerity of some of those appeals that seem more and more like
fishing expeditions trying to figure out how to improve their copypasta skills.
But I don't think we would be able to push them all into e-mails. They would still create threads and then we would wait for mods to nuke them and someone would still reply to the threads... would be a mess.
And some perspective: mods have been banning 1-2 thousand users per week recently. According to the OP there were ~30 appeal threads in ~ half a week, including bumps of older threads from before. Could be worse.