Thank you for all your responses!
Simon: I believe that's it! It's definitely incorrect to have more closing than opening divs (it's not a well-formed XHTML document). I've just installed Sigil to get familiar with the ePUB format and I'm glad to see it's basically just a set of HTML files and metadata.
Also I believe the second closing </div> (of the 2 remaining) should not follow the table, but should instead be located just before the closing </body> - in other files, the main <div class="split"> always encloses the whole chapter. I'll try fixing the ePUB file and uploading it back to the reader to see if it will help.