I now have a jenkins job running (tenth iteration, after many attempts to figure out basic shell stuff in jenkins). Config here for the moment -- going into svn when ready:
<?xml version='1.0' encoding='UTF-8'?>
<project>
<actions/>
<description>Runs a script which checks links on the Guidelines HTML output from TEIP5.</description>
<keepDependencies>false</keepDependencies>
<properties>
<jenkins.advancedqueue.AdvancedQueueSorterJobProperty plugin="PrioritySorter@2.6">
<useJobPriority>false</useJobPriority>
<priority>-1</priority>
</jenkins.advancedqueue.AdvancedQueueSorterJobProperty>
</properties>
<scm class="hudson.scm.NullSCM"/>
<canRoam>true</canRoam>
<disabled>false</disabled>
<blockBuildWhenDownstreamBuilding>false</blockBuildWhenDownstreamBuilding>
<blockBuildWhenUpstreamBuilding>false</blockBuildWhenUpstreamBuilding>
<triggers/>
<concurrentBuild>false</concurrentBuild>
<builders>
<hudson.tasks.Shell>
<command>VERSIONFILE=$JENKINS_HOME/jobs/TEIP5/workspace/VERSION
VERSION=`cat ${VERSIONFILE}`
TARGET=$JENKINS_HOME//jobs/TEIP5/lastSuccessful/archive/release/doc/tei-p5-doc/en/html/index.html
echo "Running link checking for P5 version $VERSION."
if [[ $VERSION =~ [a-z]+$ ]]; then
echo "Using configuration for pre-release version."
linkchecker --config=$JENKINS_HOME/jobs/Guidelines-Link-Check/linkcheckerrcalphabeta $TARGET
else
echo "Using configuration for release version."
linkchecker --config=$JENKINS_HOME/jobs/Guidelines-Link-Check/linkcheckerrcrelease $TARGET
fi
echo "Transforming checker report..."
saxon -s:checkResults/linkchecker-out.xml -xsl:$JENKINS_HOME/jobs/Guidelines-Link-Check/linkchecker.xsl
echo "Done!"
exit</command>
</hudson.tasks.Shell>
</builders>
<publishers>
<hudson.plugins.logparser.LogParserPublisher plugin="log-parser@1.0.8">
<unstableOnWarning>false</unstableOnWarning>
<failBuildOnError>true</failBuildOnError>
<parsingRulesPath>/var/lib/jenkins/hudson-log-parse-rules</parsingRulesPath>
</hudson.plugins.logparser.LogParserPublisher>
</publishers>
<buildWrappers/>
</project>