The quest is buggy. BW has acknowledged it on the known issues list. And there are multiple issues.
I have done it on multiple toons with various different groups. So I will share what I found to be working:
Whenever you start a new group or there is change of group composition, everyone should zone out, reset the quest and reset phase. Yes it sucks. But it worked 90% of the time in my experience (the 10% of the time it didn't work was when one group member was further bugged due to dc; re-logging fixed the problem eventually)
For both Shroud Revealed and Dark Design, I believe they were patched since initial release to allow players not on the quest (or completed the quest) to group up to help. But note the workaround on the bug list: "Replicator Droids are defeated only by group members who currently have the mission objective."
I tried it with a couple of guild mates who had already finished it, but they were unable to board the skiff at the start of the quest!
Reset your quest and phase, and zone in together with your guild mates. When you are at the platform, get your guild mates to click first and then you click. This should start the spectator mode cutscene for them and everyone should be aboard once the cutscene finishes.