Slightly related: what do you think if action_quickmod2 goes somewhere else? For example ModerationCenter_Controller.

I was playing with Display_Controller (splitting a bit action_index in more functions) and it sounds strange to have a quickmod there...

Oh, interesting question, because it appears somehow this way. But, no, I don't think mod center has anything to do, because the request doesn't happen in/from moderation center pages, does it?

For what the user can do in display or message index pages, IMO first choice would be: display or message index controllers should have actions, to handle those requests. So, yes, quickmod() and quickmod2().
If you feel it's too much for them, then a separate moderation controller: but for moderation actions, not some controller which is displaying mod center pages.

(side note: badly named as 2, cuz they have no relation with each other, but they were functions so I guess conflicts were the reason; they'd both be quickmod)