Okay, when I sync just the iterator.pickle, the bookmarks are synced perfectly between my computers, thank you very much for your help.
If you allow my curiosity, I'd like to understand why, though. As far as I can tell, the iterator.pickle has several entries for each book, one for every machine it's been opened on, each with its own path and different bookmarks, both current_page and possibly others, if I create a static bookmark. How does Calibre know to open the book on the correct page when the entry that corresponds to the machine I'm on has an outdated bookmark?