How to ground a junction box extension when using a non-metallic box?
Your inspector is right and wrong at the same time!

First off, the existing install is a violation of NEC 422.16(A), so your inspector was correct to point that out:


  (A) General. Flexible cord shall be permitted (1) for the
  connection of appliances to facilitate their frequent interchange or to prevent the transmission of noise or vibration or
  (2) to facilitate the removal or disconnection of appliances that
  are fastened in place, where the fastening means and mechanical connections are specifically designed to permit ready removal for maintenance or repair and the appliance is intended
  or identified for flexible cord connection.


As to the proposed fix, however, your inspector is confused or working from an old Code edition, as the 2014 (and 2017 AFAIK) NEC do not require a disconnecting means for a hardwired appliance if the breaker can be locked off (an electrical supply house will be able to order in lockoff devices for any modern breaker type).  This is 422.31(B) in the Code:


  (B) Appliances Rated over 300 Volt-Amperes. For permanently connected appliances rated over 300 volt-amperes,
  the branch-circuit switch or circuit breaker shall be permitted
  to serve as the disconnecting means where the switch or circuit breaker is within sight from the appliance or is lockable in
  accordance with 110.25.


So, I'd simply take an ordinary single gang metal faceplate with a 1/2" KO in it and use that instead of faffing about with a box extension that needs grounding.  (250.148 calls out metallic boxes, but not metallic faceplates on nonmetallic boxes...although it is still wise to attach a grounding pigtail to the faceplate in this case.)