For reasons I cannot fathom, if I add an even-page section break between the two, the Preface starts on Page 13. However, then the page numbering for the Preface is messed up.

I notice that the entire document is in the normal style. You are doing a lot of extra work! While I'm looking more, I would suggest (strongly) that you peruse
Why use Microsoft Word’s built-in heading styles? and How to create a table of contents in Microsoft Word. Then possibly Understanding Styles in Microsoft Word.