Thought I had posted this for review, but it turns out it's still in my tree. Anyway, I also tackled this.
We need to do one more thing, I think. Stuffing the contents inside name isn't correct. Instead, what we need to do is subclass Origin and provide the right metadata for discovery. We then want to override get_contents() to do the resource_string() based on that metadata.
Here's what I had:

class ExtensionOrigin(Origin):
    """An origin for a template in an extension.

    Version Added:
        3.0
    """

    def __init__(self, package, resource, *args, **kwargs):
        """Initialize the origin.

        Args:
            package (unicode):
                The name of the package providing the template.

            resource (unicode):
                The resource path within the package.

            *args (tuple):
                Positional arguments to pass to the parent.

            **kwargs (dict):
                Keyword arguments to pass to the parent.
        """
        self.package = package
        self.resource = resource

        super(ExtensionOrigin, self).__init__(*args, **kwargs)


class Loader(BaseLoader):
    ...

    def get_contents(self, origin):
        """Return the contents of a template.

        Args:
            origin (ExtensionOrigin):
                The origin of the template.

        Returns:
            unicode:
            The resulting template contents.
        """
        try:
            return resource_string(origin.package, origin.resource)
        except Exception:
            raise TemplateDoesNotExist(origin)

    def get_template_sources(self, template_name):
        """Load templates from enabled extensions.

        Args:
            template_name (unicode):
                The name of the template to load.

        Yields:
            ExtensionOrigin:
            Each possible location for the template.
        """
        if manager:
            resource = 'templates/%s' % template_name

            for extension_mgr in get_extension_managers():
                for extension in extension_mgr.get_enabled_extensions():
                    package = ext.info.app_name

                    yield ExtensionOrigin(
                        package=package,
                        resource=resource,
                        name='extension:%s:%s' % (package, resource),
                        template_name=template_name,
                        loader=self)

Ship It!