I dont have the time to track down everything wrong with that epub, but so far I've found that the links to the Preface and Introduction dont work in the original epub either. And you are probably using css/conversion settings that are inserting page breaks <div class="poetry"> and <p class="titlename"> which will cause links to individual poems to end up pointing to the end of the previous poem.
Do an epub to epub conversion and test the resulting epub, you will see the same set of problems.
Fix the Preface and Introduction links and move the id="poemwhatever" attribute to the <p> tag, so that the links point to the correct place.
Alternatively, use page-break-before instead of page-break-after.