How are range violations during a launch countdown handled?
As far as the FAA is concerned, it's just an airspace violation.  There is a restricted area over the center/base that extends up to 5000 feet.  This is active continuously.  There are other restricted areas that extend up to 'unlimited' that are "Intermittent by NOTAM normally 24 HRS in advance."  

So high altitude traffic is not impacted by the continuous restriction and when there is a launch the restriction is published by NOTAM in advance.  This gives ATC the ability to route traffic around the area without any significant impact.  Since the safety area extends out into international airspace, the FAA can't control it as restricted airspace.  They have been defined as FAR 91.143 airspace, which states:


  §91.143   Flight limitation in the proximity of space flight
  operations. When a Notice to Airmen (NOTAM) is issued in accordance
  with this section, no person may operate any aircraft of U.S.
  registry, or pilot any aircraft under the authority of an airman
  certificate issued by the Federal Aviation Administration, within
  areas designated in a NOTAM for space flight operation except when
  authorized by ATC.


So violation of the NOTAMed airspace is a violation of 91.143.

In my experience (5 years working launch ops) the issue usually arises with GA aircraft that want to watch.  If someone enters the area, ATC will try to contact them by radio.  There are also helicopters and or plane that can intercept and escort the aircraft clear.  Space Shuttle launches had the largest contingent of aircraft.  Some small booster ops might have one helo or a King Air to deal with intruders.  

The aircraft can also be used to get the attention of boats in the area.

Whether you scrub a launch or not depend on the launch window. I've seen them range from a few minutes to several hours.  A violator at the wrong time will cause a scrub with a short window, while you can handle the delay with a larger window.