Trying to avoid child themes. Header problems

I have a WordPress network site and each blog shares the same header navigation, but separate header layout.

The ideal solution would be to do a php include file in the header option area of theme configuration. That way, I can have the following:

navigation.php gets loaded into:
business_hdr.php
homestead_hdr.php
main_hdr.php

Then, for each sub blog, all I have to do is include the proper php header for the design I need. Then, if I ever have to change the navigation link, I just update one file...navigation.php.

The problem is, I'm not allowed to do php code in the theme options and the code doesn't recognize html include.

That only leaves me to use child themes so each blog can have the php include header code on the index.php file. That's how I'm giving each header it's own look. I had to duplicate the atahualpa folders so I can do a php include line on each of the index pages.

It's a pain to maintain. Now that there is an update available for atahualpa, I have to update a lot of instances!

Is there a better way?