After some more tinkering I was able to place a div block into a list item.
It only works when I drag a new list item element from the Add Elements panel into the existing list and then add the div block directly after. If, however, I first populate the list item with text by double clicking on it in the canvas and typing, then I can no longer place div blocks inside it even after I clear the text and the list item reverts to looking like a brand new one.