There are three elements you want to rename: Participants, Participant, and person. The other elements should all be copied unchanged. (The name of an element is in two parts: namespace URI and local name. Changing either part is best thought of as a renaming operation).
So you need four template rules. The default rule copies things unchanged:
<xsl:template match="*">
<xsl:copy>
<xsl:copy-of select="@*"/>
<xsl:apply-templates/>
</xsl:copy>
</xsl:template>
and the others do a renaming. Here is one of them:
<xsl:template match="Participants">
<ns0:Participants xmlns:ns0="http://COINS_SCHEMAS.Participants">
<xsl:copy-of select="@*"/>
<xsl:apply-templates/>
</ns0:Participants>
</xsl:template>
The others are similar.
>if there was a way to make BizTalk not worry about the prefix/namespace definitions on the records I wouldn't need to do the transform.
That's a bit like me asking my bank manager to accept instructions from anyone called Mike, regardless of the surname.
Michael Kay
http://www.saxonica.com/
Author, XSLT Programmer's Reference and XPath 2.0 Programmer's Reference