Use a Date document property mapped to a content control. Put the same control in each place.
See
Mapped Content Controls and Document Properties and
CC⁄V⁄BM & DP Tools Add-in

A separate question is whether you really need that many headers and footers. You may, but the StyleRef Field is often used to put different header/footer content in different parts of a document using the same header/footer.

One other thing to keep in mind is that your documents may have headers and footers you don't even know about, that are not displayed. These can have content. Each section has three headers and three footers. These may not be active or displayed and still have content, which sometimes can change content in other areas that are displayed!

Sections / Headers and Footers in Microsoft Word 2007-2013