Thanks for the tips, Bookworm_Girl!
I tried syncing collections, and that works. I'm not sure why annotations weren't traveling in both directions when I used the folder method, but anyway the collection method makes more sense for me. I should have read your posts more carefully the first time! I also tried deleting annotations on the Reader and then syncing, and deleted annotations were also removed in Reader Library.
I think I discovered why -- at least one reason why -- people get duplicate copies of books. Using Reader Library, I added two books that I've already read to a collection that I set to sync with my Reader. Both books were already on the device, and both were successfully added to the collection on the device. The difference was that Book 1 was a book whose annotations I had lost. I had re-copied it to the device from Reader Library to get the annotations back. Therefore, there was no dictionary log or reading history for that book on the device. After the sync, Book 1 appeared in the appropriate collection, and there was only one copy of it in the list of all books. Book 2 was a book that I had finished reading on the device after the loss of some annotations. Therefore, that book already had a reading history and dictionary log on the device. For this book, the synchronization used a new copy of the book to add it to a synchronized collection. After the sync, the copy in the collection on the device had the annotations but not the dictionary log, while the other copy still had the dictionary log. I decided to remove the book from the collection and keep the original copy on the Reader. Unfortunately, you cannot use a Reader to add or remove books to synchronized collections.
There's one other possible explanation for this behavior. I had installed Book 1 to the Reader using Reader Library, and the EPUB file was stored in the root media\books folder. I had used Calibre to install Book 2, and the original copy of that book was under media\books but in a subfolder with the author's name. I think it's unlikely that this is related to the problem of duplicate books, simply because the I think the developers of Calibre would have quickly realized that and modified how Calibre interacts with Sony Reader devices. In any case, I think I will use Reader Library to manage books on my Reader to avoid any possible conflicts.
Also, I think it's a good idea to decide on a basic organization for synchronized collections and stick to it rather than making a habit of moving synchronized books between collections.