The reason given for the restriction (which is a PITA) is that you are worried about edits that might affect the meaning of a comment thread. AFAICT, that reason is irrelevant for the case where there is no thread following the comment. That's my suggestion: As long as your comment is the latest in the thread, there should be no time limit on editing it. And as soon as someone else adds a comment you should get the notification of a new comment (dunno whether this is already done), as is done for new answers.
Also there are lots of comments on a question or answer that do not result in a real "thread", even when there are multiple comments. In my experience, most comments are one-offs or relatively unrelated to other comments: they comment on the question or answer (usually helpfully) and do not refer to other comments. Meta is the big exception (perhaps those making such rules spend too much time on Meta?).
It is really poor UI to show an active edit link for a comment that you can no longer edit. And if your comment is the most recent one, I don't see why you shouldn't be able to take your time and add or correct information incrementally.