I'm slightly surprised that you can process this input using XSLT at all, because it seems not to be well-formed XML - the <br> tags are not closed. Let's assume that's a red herring and it is well-formed.
Then the answer to your question, how to do a "slightly modified copy", is a classic XSLT design pattern. First you write an identity template that copies everything unchanged:
<xsl:template match="*">
<xsl:copy><xsl:copy-of select="@*"/><xsl:apply-templates/></xsl:copy>
</xsl:template>
then you override this with a template that modifies the elements you want to modify:
<xsl:template match="IMGOBJECT">
<img src="{FILENAME}">
<xsl:attribute name="style">
<xsl:for-each select="STYLE/PARAM">
<xsl:value-of select="concat(@attribute, ': ', .)"/>
</xsl:for-each>
</img>
</xsl:template>
(You may have to refine that but it illustrates the idea)
Michael Kay
http://www.saxonica.com/
Author, XSLT Programmer's Reference and XPath 2.0 Programmer's Reference