Get TZ abbrev for given timestamp and TZ name

Is it possible to get correct TZ abbreviation after converting column of type timestamptz ?

What I am after, sof example, is to display "2016-06-16 16:00:00-04" in "US/Pacific" timezone with target TZ abbrev. I can get this easily:

06/16/2016 01:00 pm

But I cannot get following:

06/16/2016 01:00 pm PDT

Once converted, timestamptz becomes timestamp without timezone and to_char specifier 'TZ' becomes meaningless...

Here an example of what I have tried:

SELECT
    scheduled_dt                                                                           AS scheduled_dt
  , to_char(scheduled_dt, 'TZ')                                                            AS scheduled_dt_orig_tz  
  -- correct value, but missing TZ  
  , timezone('US/Pacific', scheduled_dt)                                                   AS schedules_dt_converted_tz
  , to_char(timezone('US/Pacific', scheduled_dt), 'MM/DD/YYYY HH:MI pm')                   AS scheduled_dt_converted_tz_localized
   -- after conversion TZ is lost
  , to_char(timezone('US/Pacific', scheduled_dt), 'MM/DD/YYYY HH:MI pm TZ')                AS scheduled_dt_converted_tz_localized_missing_tz
  -- with cast, wrong TZ is displayed 
  , to_char(timezone('US/Pacific', scheduled_dt)::timestamptz, 'MM/DD/YYYY HH:MI pm TZ')   AS scheduled_dt_converted_tz_localized_wrong_tz
FROM orders
LIMIT 5  

and sample output:

"scheduled_dt","scheduled_dt_orig_tz","schedules_dt_converted_tz","scheduled_dt_converted_tz_localized","scheduled_dt_converted_tz_localized_missing_tz","scheduled_dt_converted_tz_localized_wrong_tz"
"2016-06-16 16:00:00-04","EDT","2016-06-16 13:00:00","06/16/2016 01:00 pm","06/16/2016 01:00 pm ","06/16/2016 01:00 pm EDT"
"2014-07-15 08:00:00-04","EDT","2014-07-15 05:00:00","07/15/2014 05:00 am","07/15/2014 05:00 am ","07/15/2014 05:00 am EDT"
"2012-11-27 10:15:00-05","EST","2012-11-27 07:15:00","11/27/2012 07:15 am","11/27/2012 07:15 am ","11/27/2012 07:15 am EST"
"2011-03-02 08:30:00-05","EST","2011-03-02 05:30:00","03/02/2011 05:30 am","03/02/2011 05:30 am ","03/02/2011 05:30 am EST"
"2016-02-12 14:23:09-05","EST","2016-02-12 11:23:09","02/12/2016 11:23 am","02/12/2016 11:23 am ","02/12/2016 11:23 am EST"