[headless] Several tests on java.awt started to fail in headless mode on JDK7u76 and JDK8u31

This is a mirror of JCK-7303911, please see JCK-7303911 for the details.
Shortly speaking a bunch of JCK7 and JCK8 tests started to fail in headless mode on 7u76 and 8u31 builds.
Reporter of the original issue provided JDK7u76b07 and JDK8u31b07 as the particular problematic builds.

There might be a duplicate of this exact problem filed already.

Verified the following tests failing with JDK8u31b07
  * api/java_awt/Event/InputMethodEvent/descriptions.html#InputMethodEventCtorTests: Failed. test cases: 24; passed: 2; failed: 22; first test case failure: committedCharacterCountInvalidLow
  * api/java_awt/Event/InputMethodEvent/descriptions.html#InputMethodEventOtherTests2: Failed. test cases: 9; all failed; first test case failure: getCommittedCharacterCountTests

Other failing tests and affected client areas could be found in JCK-7303911