Current Shenandoah control thread runs with the default priority (NearMaxPriority):

ShenandoahControlThread::ShenandoahControlThread():
  create_and_start();

ConcurrentGCThread:
  // Create and start the thread (setting it's priority.)
  void create_and_start(ThreadPriority prio = NearMaxPriority);

CMS and others are able to use critical thread priority, for example:

  create_and_start(UseCriticalCMSThreadPriority ? CriticalPriority : NearMaxPriority);

We should consider doing the same for Shenandoah.