A co-worker told me that every build in Jenkins has "actions" associated with it and that Jenkins plugins do their magic via actions.  I was able to find all actions of my actions with build.getActions().  I then looped through the actions until I got LogParserAction which is the action supplied by the Jenkins Log Parser plugin.
I then looked through the source code of LogParserAction.class to find the method getErrorLinksFile().  With this method I was able to get the text of the parsed log.  A similar method called getWarningLinksFile() is available for the warnings and another is available for info.
I then looped through the text on \n character and applied some regexs to make it look how I wanted.  Important parts of the code are below.  Looks better if you view it as HTML in Notepad++
%>
    <TABLE width="100%">
        <TR>
            <TD class="bg1" colspan="2">ERRORS</TD>
        </TR>
<%
    def publisher = null
    for(iter in project.getPublishersList()){
        if(iter.getDescriptor().getDisplayName().equals("Editable Email Notification")){
            publisher = iter
            break
        }
    }
    if(publisher != null){
        def logParserResult
        //Get the LogParserAction from Jenkins
        for(action in build.getActions()){
            if(action.toString().contains("LogParserAction")){
                //Get the LogParserResult from the LogParserAction
                logParserResult = action.getResult()
                break
            }
        }
        //Get the ErrorLinksFile from the LogParserResult
        def errorLinksFile = new File(logParserResult.getErrorLinksFile())
        //Rewrite the URL so it directs to something useful
        pattern = ~/<a.*?><font.*?>/
        def errorList = []
        for(line in errorLinksFile.getText().split("\n")){
            //All errors have a link, so this makes sure no superfluous text is displayed
            if(!line.contains("href")){
                continue
            }
            errorList.add(line.replaceAll(pattern, "<a href="+ rooturl + build.url + "parsed_console/?\">").minus("</font>"))
        }
%>
        <TR>
            <TD class="bg2" colspan="2">Total : ${errorList.count{it}} error(s)</TD>
        </TR>
<%
        for(error in errorList){
%>
        <TR>
            <TD class="errors" colspan="2">${error}</TD>
        </TR>
<%
        }
%>
    </TABLE>