I think a comment is a good way to do this.
For the author of the answer, it will notify them. Even if the comment ends up deleted, they will have received the information that you found their answer useful in this way.
For others, the comment is generally useful (there are tons of comments that say things like "this is the best answer I have ever read on this site" or "I signed up for this site just so I could upvote this") as a measure of the quality of the answer. It may also be helpful to people who have read the whole answer, if you include a link to the book, so that people can read more on the topic. That's especially true if you expand on the answer or use it as a starting point for your own work in the book.
Sure, some of the answer authors won't be active any more -- but in that case you'd be unlikely to reach them any other way anyway. And sure, some of the comments might get deleted on a site that doesn't like "this is a great answer" comments. But I think that's an ok outcome if the authors saw the comment before it was deleted - comments are ephemeral.
The comment has the least impact on everybody else -- a chat room with 14 people who don't know each other feels odd to me, a meta post on each relevant site with links to the answers brings in people who otherwise wouldn't read those answers, and so on -- while at the same time being most likely to reach the original answer authors you want to reach.