How to override an admin theme template?

You can declare a new primary theme for your admin area by customizing config (e.g. app/etc/local.xml) with the following:

<config>
    <stores>
        <admin>
            <design>
                <theme>
                    <default>your_theme</default>
                </theme>
            </design>
        </admin>
    </stores>
</config>

This will just set another level of fallback, and you can copy this and other custom templates/layout/etc under the right path in app/design/adminhtml/default/your_theme/

Go to your extension's admin layout file or create one if you don't have yet.

default/default/layout/your_xml.xml

and add this in default section:

<layout>
    <default>
       <reference name="root">
          <action method="setTemplate">
              <template>your_path/page.phtml</template>
          </action>
       </reference>
    </default>
</layout>

I haven't tested but should work. Good luck.