Punctuation

Q. Hello, CMOS! How do I punctuate when a question mark precedes a semicolon: “Why are you writing Matt’s evaluation?; he works in Emily’s office.” CMOS 6.54 tells us what to do when the first of the closely related sentences ends with a period; it looks funny when it ends with a question mark. Clearly, I could just separate it into two sentences. But can this construction be saved?

A. It cannot be saved! Just start a new sentence.