I have resolved this issue by figuring out how to edit the view.xsl file.  I
placed the signature block inside the xsl:if tags that control display of the
section, but not within the div tags that contain the section content itself:

<xsl:template ...> = the greater container for the section
   <xsl:if ...> = the condition that controls hide/show of the section
       <div ...> = the div containing the section controls
       </div>
       <div ...> = the signature block div
       </div>
   </xsl:if>
</xsl:template>

Warning: I have been developing using VisualStudio and the InfoPath
designer. As feared, the InfoPath designer mangles direct edits of the
view.xsl files such as the one above, so proceed with caution and make a
backup copy of the xsl contained within the view.xsl files before you make
any changes in the InfoPath designer. (If there's a way to prevent InfoPath
from mangling code similar to the options available in the VisualStudio
designer, I haven't found it!)

~ Tillman