Another problem that many people have when reciting poetry is that they pause at the end of a line. Unless it has a period, it generally isnt meant to be paused at.
This is especially true of some forms such as Tanka and Haiku where the line lengths are based on syllables. It might help in reading the poem aloud before an audience to convert the poem into paragraph form so
that you dont get caught in this trap. Admittedly, this is more likely to happen in reading someone elses poetry than in reading your own, but you might still find it easier.
This technique can also help to alleviate the singsong problem. If the rhymes are not as apparent because they are not at the end of lines, one is less likely to stress