OK, I found something that works. It’s a plugin called Widgets on Pages. It allows me to have a widget sidebar that can be used anywhere with a shortcode. I’ve added that to the header area to the right of the logo.

I have this set up on the staging site now and it looks like it is working on all pages with the Jetpack Facebook Feed plugin. Note that the home page is still using the default header, but if you go to any subpages on the site, you can see the default header I’ve assigned working. If you can make the home page use the default header, that would be better just to see it there, but I’m not sure how to do that any more.