Well, I finally found the issue that was causing this, and I'm posting a detail answer in case someone else has these issues.
I tried jmap while the process was acting up, but this usually caused the jvm to hang further, and I would have to run it with --force. This resulted in heap dumps that seemed to be missing a lot of data, or at least missing the references between them. For analysis, I tried jhat, which presents a lot of data but not much in the way of how to interpret it. Secondly, I tried the eclipse-based memory analysis tool ( http://www.eclipse.org/mat/ ), which showed that the heap was mostly classes related to tomcat.
The issue was that jmap was not reporting the actual state of the application, and was only catching the classes on shutdown, which was mostly tomcat classes.
I tried a few more times, and noticed that there were some very high counts of model objects (actually 2-3x more than were marked public in the database).
Using this I analyzed the slow query logs, and a few unrelated performance problems. I tried extra-lazy loading ( http://docs.jboss.org/hibernate/core/3.3/reference/en/html/performance.html ), as well as replacing a few hibernate operations with direct jdbc queries (mostly where it was dealing with loading and operating on large collections -- the jdbc replacements just worked directly on the join tables), and replaced some other inefficient queries that mysql was logging.
These steps improved pieces of the frontend performance, but still did not address the issue of the leak, the app was still unstable and acting unpredictably.
Finally, I found the option: -XX:+HeapDumpOnOutOfMemoryError . This finally produced a very large (~6.5GB) hprof file that accurately showed the state of the application. Ironically, the file was so large that jhat could not anaylze it, even on a box with 16gb of ram. Fortunately, MAT was able to produce some nice looking graphs and showed some better data.
This time what stuck out was a single quartz thread was taking up 4.5GB of the 6GB of heap, and the majority of that was a hibernate StatefulPersistenceContext ( https://www.hibernate.org/hib%5Fdocs/v3/api/org/hibernate/engine/StatefulPersistenceContext.html ). This class is used by hibernate internally as its primary cache (i had disabled the second-level and query-caches backed by EHCache).
This class is used to enable most of the features of hibernate, so it can't be directly disabled (you can work around it directly, but spring doesn't support stateless session) , and i would be very surprised if this had such a major memory leak in a mature product. So why was it leaking now?
Well, it was a combination of things:
The quartz thread pool instantiates with certain things being threadLocal, spring was injecting a session factory in, that was creating a session at the start of the quartz threads lifecycle, which was then being reused to run the various quartz jobs that used the hibernate session. Hibernate then was caching in the session, which is its expected behavior.
The problem then is that the thread pool was never releasing the session, so hibernate was staying resident and maintaining the cache for the lifecycle of the session. Since this was using springs hibernate template support, there was no explicit use of the sessions (we are using a dao -> manager -> driver -> quartz-job hierarchy, the dao is injected with hibernate configs through spring, so the operations are done directly on the templates).
So the session was never being closed, hibernate was maintaining references to the cache objects, so they were never being garbage collected, so each time a new job ran it would just keep filling up the cache local to the thread, so there was not even any sharing between the different jobs. Also since this is a write-intensive job (very little reading), the cache was mostly wasted, so the objects kept getting created.
The solution: create a dao method that explicitly calls session.flush() and session.clear(), and invoke that method at the beginning of each job.
The app has been running for a few days now with no monitoring issues, memory errors or restarts.
Thanks for everyone's help on this, it was a pretty tricky bug to track down, as everything was doing exactly what it was supposed to, but in the end a 3 line method managed to fix all the problems.