Modify attribute value in XSLT and call template again for second time

I'm working with the SharePoint content query web part. I have an HTML output which is desired to be

<ul>
<li>
    <img src="{RowAttribute-Url}" />
</li>
<li>
    <img src="{RowAttribute-Url}" />
</li>
</ul>
<table>
<tr>
<td>{RowAttribute-Title}</td>
<td>{RowAttribute-Title}</td>
</tr>
</table>

and the input xml for the CQWP is

<dsQueryResponse>
<Rows>
<Row ID="1" Title="Jane Doe" Modified="2010-10-14 14:05:14" Author="" Editor="" Created="2010-10-14 11:50:35"  ArticleStartDate="2010-10-01 00:00:00" Style="OutputTemplateName" GroupStyle="DefaultHeader" __begincolumn="True" __begingroup="False"></Row>
<Row ID="2" Title="John Doe" Modified="2010-10-14 14:05:29" Author="" Editor="" Created="2010-10-14 13:17:10" ArticleStartDate="2010-10-01 00:00:00"  Style="OutputTemplateName" GroupStyle="DefaultHeader" __begincolumn="False" __begingroup="False"></Row>
</Rows>
</dsQueryResponse>

So you can see that the web part will "tell" the xslt that it should render a particular style or output template. I'd like to re-run a second template on the rows and I thought that the easiest way to do this would be to replace the style attribute after the first run-through.

The first run through I'd like to render a series of li tags for each row and the second go through i'd like to do trs.

Is it possible to use xsl-copy to replace the "OutputTemplateName" prior to calling the ItemStyle template again?

Here is the xslt for the outer and inner stylesheets (inner being the itemstyles)

<xsl:template name="OuterTemplate">
    <xsl:variable name="Rows" select="/dsQueryResponse/Rows/Row" />
    <xsl:variable name="RowCount" select="count($Rows)" />
    <xsl:variable name="IsEmpty" select="$RowCount = 0" />
  <div id="container">
    <div id="inner-container">
                <xsl:choose>
                    <xsl:when test="$IsEmpty">
                         <xsl:call-template name="OuterTemplate.Empty" >
                             <xsl:with-param name="EditMode" select="$cbq_iseditmode" />
                         </xsl:call-template>
                    </xsl:when>
                    <xsl:otherwise>
                         <xsl:call-template name="OuterTemplate.Body">
                             <xsl:with-param name="Rows" select="$Rows" />
                             <xsl:with-param name="FirstRow" select="1" />
                             <xsl:with-param name="LastRow" select="$RowCount" />
                        </xsl:call-template>                         
                    </xsl:otherwise>
                </xsl:choose>        
    </div>
  </div>
</xsl:template>


<xsl:template name="OuterTemplate.Body">
    <xsl:param name="Rows" />
    <xsl:param name="FirstRow" />
    <xsl:param name="LastRow" />
  <div id="container-rotator">
    <ul>
      <xsl:for-each select="$Rows">
          <xsl:variable name="CurPosition" select="position()" />
          <xsl:if test="($CurPosition &gt;= $FirstRow and $CurPosition &lt;= $LastRow)">              
              <xsl:call-template name="OuterTemplate.CallItemTemplate">
                  <xsl:with-param name="CurPosition" select="$CurPosition" />
              </xsl:call-template>               
          </xsl:if>
      </xsl:for-each>        
    </ul>
  </div>
  <h5>       
    <xsl:value-of select="ddwrt:FormatDateTime(string(/dsQueryResponse/Rows/Row[1]/@ArticleStartDate), 1033, 'MMMM')"/></h5>
  <table>
    <!-- before calling this foreach.. would i do the copy? -->
    <xsl:for-each select="$Rows">
      <xsl:variable name="CurPosition" select="position()" />
      <xsl:if test="($CurPosition &gt;= $FirstRow and $CurPosition &lt;= $LastRow)">
        <xsl:call-template name="OuterTemplate.CallItemTemplate">
          <xsl:with-param name="CurPosition" select="$CurPosition" />
        </xsl:call-template>            
      </xsl:if>
    </xsl:for-each>
  </table>
  <div>
    <a title="" href="/sites/sitename/Pages/page.aspx" target="">A Page Link</a>
  </div>
  <div>
    <a href="#">Another Page</a>
  </div>
</xsl:template>

And then the item template is below this is the template that i'd like to nearly duplicate but instead use trs and also provide a new "Style"

<xsl:template name="OutputTemplateName" match="Row[@Style='OutputTemplateName']" mode="itemstyle">
    <xsl:param name="CurPos" />
    <xsl:choose>      
    <xsl:when test="$CurPos = 1">
      <li class="show">
        <img src="{$SafeImageUrl}" />
      </li> 
    </xsl:when>
    <xsl:otherwise>
      <li>
         <img src="{$SafeImageUrl}" />
      </li>      
    </xsl:otherwise>
    </xsl:choose>   
  </xsl:template>

So, in summary, I have a series of rows that i'd like to put into firstly, an unordered list and then later into a table… all of this is outputted as HTML but i can only send it into one outer transform.

Even any conceptual suggestions would be helpful. I'll continue to update this post as I discover more.

BELOW I USED THE ACCEPTED ANSWER TO DO THE FOLLOWING **

Using the answer below I'll illustrate the changes needed to the above.

In the main wrapper xslt I did the following.

<xsl:template name="OuterTemplate.CallItemTemplate">
<xsl:param name="CurPosition" />
<xsl:param name="Mode" />
<xsl:choose>
  <xsl:when test="$Mode = 'table'">
    <xsl:apply-templates select="." mode="table">
      <xsl:with-param name="CurPos" select="$CurPosition" />
    </xsl:apply-templates>
  </xsl:when>
  <xsl:when test="$Mode = 'listitem'">
    <xsl:apply-templates select="." mode="listitem">
      <xsl:with-param name="CurPos" select="$CurPosition" />
    </xsl:apply-templates>
  </xsl:when>
  <xsl:otherwise>
    <xsl:apply-templates select="." mode="itemstyle">
    </xsl:apply-templates>
  </xsl:otherwise>
</xsl:choose>

And then i have two item templates instead of one.

<xsl:template name="TemplateNameList" match="Row[@Style='TemplateName']" mode="listitem">
<xsl:param name="CurPos" />
<xsl:variable name="SafeImageUrl">
  <xsl:call-template name="OuterTemplate.GetSafeStaticUrl">
    <xsl:with-param name="UrlColumnName" select="'ImageUrl'"/>
  </xsl:call-template>
</xsl:variable>
<xsl:choose>
  <xsl:when test="$CurPos = 1">
    <li class="show">
      <img src="{$SafeImageUrl}" />
    </li>
  </xsl:when>
  <xsl:otherwise>
    <li>
      <img src="{$SafeImageUrl}" />
    </li>
  </xsl:otherwise>
</xsl:choose>