I think part of the issue here is we don't have the mechanics, culture and workflow a regular site has. On a normal site, there's a meta, but a meta meta is just silly.
I've done these mass retags elsewhere. I agree that chat's not a visible enough forum (in the sense of place) for it.
Compromises are fun. They make no one happy. I do realise that one question per retag on meta for meta seems... a bit annoying. I'd like to propose a compromise - that we have a omnibus question for cleanups. We could use the community wiki option ('cause ironically, this feels close to what it's designed for) so no one needs to worry about rep loss and rep gain, and use answers to propose tags for clean ups.
As for the actual clean ups -
Flooding the front page is impolite. I've done tag cleanups involving thousands of posts. I did these a few at a time - on SU maybe 5-6 an hour over several months, but I always checked to see if my old posts had sunk down, and I also deleted or closed as needed. It's possible to keep up without flooding the front page, honest!
It's also worth remembering, while tags are a form of technical debt - they're painfully hard to fix up and not exactly time sensitive. It's probably a better use of your time to fix them as you come across than targeting specific tags, until we get a cool tool to fix it. In some of these cases, pruning tags and merging might be an option too.
I also noticed that folks were focusing on tags (for maximum velocity?). If you're fixing tags, do try to fix other issues with the post as well.
Finally while I do realise some of y'all are trying your best to bring order to chaos - meta is inherently messy since it involves, well, meta. That said if your primary goal is curation and cleanup... you're missing out on a lot.