Found one Java-level deadlock:
=============================
"Handling GET //api/python : RequestHandlerThread[#18106]":
  waiting to lock monitor 0x0000000000e4c080 (object 0x000000054239ebc0, a hudson.model.Hudson),
  which is held by "Handling POST /computer/lp-pure-ha19/configSubmit : RequestHandlerThread[#17566]"
"Handling POST /computer/lp-pure-ha19/configSubmit : RequestHandlerThread[#17566]":
  waiting to lock monitor 0x00000000030bf190 (object 0x0000000542d6bc78, a java.lang.Object),
  which is held by "PeriodicResourceAllocationTask thread"
"PeriodicResourceAllocationTask thread":
  waiting to lock monitor 0x0000000000e4c080 (object 0x000000054239ebc0, a hudson.model.Hudson),
  which is held by "Handling POST /computer/lp-pure-ha19/configSubmit : RequestHandlerThread[#17566]"

        at jenkins.model.Jenkins.save(Jenkins.java:2513)
        - waiting to lock <0x000000054239ebc0> (a hudson.model.Hudson)
        at hudson.model.Node.setTemporaryOfflineCause(Node.java:210)
        at hudson.model.Computer.setNode(Computer.java:613)
        at hudson.slaves.SlaveComputer.setNode(SlaveComputer.java:514)
        at hudson.model.AbstractCIBase.updateComputer(AbstractCIBase.java:116)
        at hudson.model.AbstractCIBase.updateComputerList(AbstractCIBase.java:174)
        - locked <0x0000000542d6bc78> (a java.lang.Object)
        at jenkins.model.Jenkins.updateComputerList(Jenkins.java:1113)
        at jenkins.model.Jenkins.setNodes(Jenkins.java:1621)

Jenkins.getInstance().setNodes(newNodes);