There is an easy fix. Make the quest repeatable, and give it a reward that people want. Say 2x elite commendations and 10x basic commendations per day.
Then people will do it.
It is a very very poor design decision to make a difficult non-repeatable heroic that needs four people the final part of this quest chain. Sack whoever came up with the idea because they have no *********** idea what they are doing and should not be working on a MMO anywhere.
This ^^ +1