So, found some more interesting tidbits. Mod_jk is very particular about the network packets it receives:
So, the recommended fix (https://jira.jboss.org/browse/JBPAPP-366) is to move to the JBossWeb Native, aka the Apache Portable Runtime. The installation couldn’t be simpler – drop in the new files into /bin/native, and restart (see http://community.jboss.org/wiki/HowToAddAprToJBoss).
Long story short, the APR replaces the out-of-the-box way that JBoss handles AJP and HTTP requests. Its faster, and apparently doesn’t have the mod_jk network packet issues. I’ve installed on both Test and Prod, and the app appears...fast and stable.
Not declaring victory, but its close.
EDIT: At this point, all seems well, so I'm going to consider the issue closed.