It’s impractical to expose an API like innerHTML from within XSLT.

Instead, Saxon-JS leverages the existing mechanism for producing result documents xsl:result-document:

<xsl:result-document href="#schedule">
  <xsl:apply-templates select="ixsl:page()/html"/>
</xsl:result-document>

If the href attribute is a same-document fragment identifier, the resulting output is appended to the element with the corresponding ID.

The extension method ixsl:replace-content instructs the processor to replace the content, rather than appending to it:

<xsl:result-document href="#schedule" method="ixsl:replace-content">
  <xsl:apply-templates select="ixsl:page()/html"/>
</xsl:result-document>

(It’s possible to write to any element, even elements that don’t have IDs, by making them the context node first.)