It is an SEO tactic that if you want only a header image instead of displaying the title and tagline, you can use "alt" text instead and Google will count it as <h1>.

<h1>
  <a href="http://example.com">
    <img src="header.png" alt="Your Site Name" />
  </a>
</h1>

How would I implement all the parts (the h1, the link, the image, and the alternate text) in an SEO friendly way in Atahualpa?

You could put code like that in the Configure Header Area box or you could add a new widget area or areas in that box and add that code to a text widget.