In case this issue happens to someone else, here's the solution. I had misspecified the spring dataSource bean. It should have been
<bean id="dataSource" class="org.springframework.jndi.JndiObjectFactoryBean">
<property name="jndiName">
<value>java:comp/env/jdbc/ProcessEngine</value>
</property>
</bean>
Also, I moved the <Resource> section from server.xml to context.xml.
Best,
Dan