<xsl:template match="Root">
        <DG>
            <xsl:apply-templates select="@*|node()"/>
        </DG>
    </xsl:template>

I need all of the other elements to come over as
well and I need to rename those elements.

yes that's what the
 <xsl:apply-templates select="*[not(self::title or self::subtitle)]"/>
is doing, applying your templates to all the child elements.
Sounds like you don't want document to go to document though so change
 <xsl:copy>  to <D>

and when I said

you just need a standard identity template,

read that as "you just need the templates doing whatever transformation
they are doing"

David