You already got it, "page_content_heading". You just need to reference it rather than adding it over again
<reference name="page_content_heading">
<action method="setTemplate"><template>cms/headers/custom.phtml</template></action>
</reference>
On a similar topic, if you're literally just looking to add a class to the file, may I recommend using the original template file (copied to your theme of course) and adding the class conditionally.
Somewhere in your template file:
<?php if ($this->getData('added_class')): ?><?php echo $this->getData('added_class') ?><?php endif ?>
Then, you can add whatever class you want with a XML layout update:
<reference name="page_content_heading">
<action method="setData"><key>added_class</key><val>YOUR_CLASS_NAME</val></action>
</reference>
That way you don't need to have a whole bunch of different .phtml files for the same purpose should you need to start adding different classes per CMS page.
On ANOTHER note... you could just add a class to the body tag without the need to customize any view script.
<reference name="root">
<action method="addBodyClass"><class>YOU_CLASS_NAME</class></action>
</reference>
Then in your CSS file target the page header using the body class as well:
.YOUR_BODY_CLASS .page-title h1{/* style rules */}