Could you talk to the poet about it? The varying lengths of the different components may have been a structural and rhythmic choice on their part, not unlike how a designer makes decisions about layout and pace in their typography. By talking to them, you'll be able to make a better interpretation of their creative intentions, and use that interpretation to inform your own decisions.

If you mark beginnings clearly (but not obtrusively), then pauses will not be mistaken for endings.

Traditionally, verse typography has conventions for this, by capitalizing the first letter of a line, putting paragraph spacing between verses, and using raised caps or small caps at the start of sections/the whole.

Nick Shinn hit the nail on the head. Mark the beginnings (section changes, whatever) and don't worry about the spaces. Here's an article with some other options:
http://www.thebookdesigner.com/2010/06/book-design-8-solutions-to-the-te...

Thanks for your suggestions. They are all excellent ones, but unfortunately not quite what I was after; I think I need to explain my problem more clearly. First of all, I am the poet—so my lack of objectivity may be part of the problem! Essentially this is just a variation of the orphans/widows vs. uneven pages dilemma, but the downsides of each option are magnified due to the particular form of the poem.

The issue is not clarity but a smooth reading experience. Large spaces at the bottoms of certain pages visually gives more importance to those breaks, even though other elements in the design make it perfectly obvious that this is not intended. The alternative of separating a first or last line from the rest of its section also takes away from the experience of that section as a single unit. (The section lengths range from about one quarter of a page to a whole page.)

I’m not trying to achieve square pages, just pages that end in the same general range. The best solution I’ve come up with is to force a page break early only to avoid the following two situations: 1) having a verse break across a page; or 2) having a single first or last line of a section alone at the bottom or top of a page. But it still doesn’t look great to me, as most pages end close to the bottom margin but some over an inch higher. (It’s a 6x9 in. book) Perhaps going past the margin in those cases would be preferable, but I’m not crazy about that either.