It turns out that the arguments needed to be at the start of the line. The following works:
SOLR="$JAVABIN -Xmx7168m -Xms1024m -Dsolr.solr.home=$SOLR_HOME -Djetty.logs=$INSTALL_PATH/logs/ -Djetty.home=$INSTALL_PATH/ -jar $INSTALL_PATH/start.jar $INSTALL_PATH/etc/jetty.xml"