What you want to do may be able to be done. It will depend on the ability of a macro to determine what it is that gets copied. Headers and footers are stored in section marks. There is one at the end of every document, but may be more in the middle. Sections / Headers and Footers in Microsoft Word (Ribbon Versions) If everything is one section, it should be relatively easy. That is not my forte' though.

However, I would suggest a paradigm shift for your new templates: use modular components stored in one or two locations. Build your templates using those components in a way that lets them be updated automatically by changes in the base.

I would suggest AutoText entries holding your letterhead, etc. Store those in a Global Template.

Then use an AutoText field to put the components into the templates. Finally, put an AutoNew macro in the templates to either lock or unlink the AutoText fields. Next time, you will need to only change the AutoText entries. All of the templates will update automatically when they are used to create new documents.
Automated Boilerplate Using Microsoft Word

I use something a bit more complex, in that I have a single document that contains parts marked by bookmarks. An AutoNew macro in each template calls them into the new document at a bookmarked location in the template. AutoText is easier but I had this set up before I realized that.

For documents based on my letterhead template, an Autonew macro tests the new document's template's name against a document variable that contains the name of the template that has the up-to-date material. If the document is based on any template other than that base one, the material is copied from the base one into the new document, replacing existing headers, footers, and styles. Because of the styles, I think that is a bit better than AutoText, but not a great deal better.