Thanks! This was counter-intuitive, but lowering the JVM memory settings worked. I made sure all of them were lower than the maximum memory on the server. Before, I was trying to raise them to meet Jaspersoft's minimum requirements.
My new settings:
export JAVA_OPTS="$JAVA_OPTS -Xms256m -Xmx512m -XX:PermSize=32m -XX:MaxPermSize=256m -Xss2m -XX:+UseConcMarkSweepGC -XX:+CMSClassUnloadingEnabled"
(not sure about Jaspersoft performance, but Tomcat now runs).