Oh, the text boundaries things was a good tip! It looks like each line of text has its own boundary around it (and each is a different width). As opposed to a normal document where the text all flows within one boundary. I don't see anything that indicates any rogue text boxes or shapes, but that text boundary things is a definite issue.
What would be causing that? I don't know a thing about how text boundaries are created or controlled. (I mostly work in InDesign, not Word).
I think the most obvious answer is to start from scratch, but it took me forever to get the document set up do be designed differently on pages after page 1 (without including any more than one page in the template), so I'd really rather resolve it from within the existing doc.
ETA:
Here's a screenshot of how the text boundaries look: