Everything is ok in edit mode, for what ever additional wrapper reasons:
but when I click my way out of edit mode, the page breaks:
In FireBug, I added a </div> tag to the page's source code (which is perfectly ok when no CQWP is added to the page) and this fixes the problem:
In real life, this obviously won't do. So as a workaround, I added a table element to the Page Layout code, inside the div-elements as a wrapper for the web part zones:
<div class="ms-webpart-zone ms-fullWidth">
Not an especially pretty insert, but the easiest fix I came up with for now.