What noise reduction measures were taken in the time between hush kits and chevrons?
Generally speaking one is an add on and the other is integrated into the design. Over the years the FAA has implemented progressively more stringent noise regulations both for aircraft that are flying as well as to the full certification process. The changes came in stages and have been progressively altered for the past 30 or so years take a look at §36.103   Noise limits for the current regulation .  You can find some of the FAA legislation here and the full text of the relevant FAR's here. As such newer engines will incorporate noise mitigation directly into the design as they need to pass the certification process. However in cases relating to older designs it may be cost effective to design an attachment (like a hush kit) that can be added to an existing engine to comply with regulations since the engine was certified at a time that the regulations were far more relaxed. Due to the letter of the law planes can be grounded for being non compliant so a hush kit may be cheaper than a new plane. For example this was the case with the Lear 23 which had required hush kits.

Interestingly at least one patent for a hush kit stresses that it is for an existing engine design.  


  BACKGROUND OF THE INVENTION 
  
  The present invention relates generally to
  jet aircraft turbine engines and, more specifically, to a hush kit for
  use on an existing engine and airframe.


You can similarly find the patent for the chevron here. Which describes it more as part of the engine than as an add on.