As a moderator I would rather see atomic flag groups -- a way to indicate that several comments are part of the same "incident", with mods able to handle them together. (This is what you suggest in your last bullet.)
Flagging comments individually is tedious for the flagger, as noted in this question. Flagging the post when not all comments should be purged is tedious for the mods, as we have to figure out which ones you meant. (And sometimes what flaggers say is "all but the last two are obsolete", but then we have to look at timestamps because more came in after you flagged.)
I want users to be able to check off #s 4, 6, 9-14, 17-39, and 42 and tell us "those ones right there should all go", and I want a mod who agrees to be able to click "make it so!" and have it be so. Atomic flag groups would be resilient in the face of newer comments, unlike my earlier example. Because it's a post flag (not comment flags) we can easily see who's flagging, to know if it's a participant in the thread, the author of the post, or somebody else. (Sometimes that matters.)
A design that supports atomic comment flags could also enable moderators to make comment-moderation one-pass instead of two-pass.
We'd need a UI element for "I wanna flag some comments together", one for "I'm done; submit that" (also cancel), and something in between to choose the comments. For the "something in between", maybe it's just the flag control but in this mode it turns them red or something so the user can see what's in the group and then it all resets when the user submits the flag or aborts. Or maybe it's a new flag type on posts that brings up the comments in the flag dialogue for selection. Y'all have people who are way better at UI design than I am; these are just some initial thoughts.
On the moderator side, we need a way to view the whole comment thread but with the flagged comments being marked somehow. We don't have this now, and it's a real hassle -- we can see the list of flagged comments, or click through to see the whole thread (necessary for context for all but the rudest of comments) without the flagged ones being marked, but we can't easily see everything. (The flagged comments are listed at the bottom of the page, but try managing a 15-comment thread with 6 or 7 flags.) In either the current interface or the atomic-flag-groups interface, we don't want to show just the selected comments and ask for a judgement; in addition to needing context, too often I've seen people try to weaponize flags to suppress the other side of an argument.