JBoss EAP becomes unresponsive with threads blocking in org.jboss.logmanager.handlers.WriterHandler

Issue

JBoss EAP 6.4 becomes slow/unresponsive with many threads blocking on org.jboss.logmanager.handlers.WriterHandler as in:

"http-/127.0.0.1:8080-244" daemon prio=10 tid=0x00002ac15439f800 nid=0x2e45 waiting for monitor entry [0x00002ac1750cc000]
   java.lang.Thread.State: BLOCKED (on object monitor)
    at org.jboss.logmanager.handlers.WriterHandler.doPublish(WriterHandler.java:59)
    - waiting to lock <0x000000040002d8b0> (a java.lang.Object)
    at org.jboss.logmanager.ExtHandler.publish(ExtHandler.java:79)
    at org.jboss.logmanager.LoggerNode.publish(LoggerNode.java:292)
    at org.jboss.logmanager.LoggerNode.publish(LoggerNode.java:300)
    at org.jboss.logmanager.LoggerNode.publish(LoggerNode.java:300)
    at org.jboss.logmanager.LoggerNode.publish(LoggerNode.java:300)
    at org.jboss.logmanager.LoggerNode.publish(LoggerNode.java:300)
    at org.jboss.logmanager.LoggerNode.publish(LoggerNode.java:300)
    at org.jboss.logmanager.Logger.logRaw(Logger.java:721)
    at org.apache.log4j.Category.callAppenders(Category.java:66)
    at org.apache.log4j.Category.forcedLog(Category.java:118)
    at org.apache.log4j.Category.info(Category.java:226)