This round of #HangTrek is now #HangTrekSolved! @Zotmeister has correctly identified the phrase:
SOULLESS MINIONS OF ORTHODOXY
They hounded the work, and plagued the existance, of Dr. Elias Geiger. You can learn almost nothing about them in the DS9 episdoe "In The Cards" (S5E25), quite possibly my favourite episode of #StarTrek.
I hope everyone enjoyed this puzzle, I loved putting it together! What a fab idea - thank you @chrysomeles
As the winner of this #puzzle, it's up to Adam to run the next game or nominate someone else to do so.