That is weird that the first sword didn't damage him. Knocked it out twice last night with two different groups and each time I did it with the first sword.I can confirm this works on Ps4/ps3 as i have had friends who have done it tried it and said it worked fine they said you have to close app or something ? but yeh this my video and here is more detailed guide if it isnt working for you:
All six of us got in an Xbox live party chat but we were all in orbit by ourselves not in a group. Then one person loaded up the crota CP by himself. This ensures he is actually the host who loaded up the map not just the fireteam leader (promoting someone to fireteam leader doesn't always work but doing this works 100% of the time). After he was in the game alone he invited the party to the game and we all joined and he revived us.
The we proceed to play as normal from top left, take out the sword bearer ect. The host had the game minimized and pressed start to bring up the "quit" game option from the main xbox menu. As soon as Crota goes to his knees we told him "now" and then he selected quit.
Easy as that. Crota will then stay on his knees forever. The first sword won't do any damage to crota for some reason but the second sword will and if you get to crota quick enough with the second sword you can kill him without even needing to kill a 3rd sword bearer.
What we did was after he quit the game and crota was stuck on his knees, we went into the left room and ignored the second sword bearer until the guy who quit rejoined the game. After we revived him back in the game, we killed the 2nd sword bearer and then killed crota.
I can also confirm this will work even if crota goes right side. The second time we did it on our alts we took too long to get crota down at the beginning and he took off right. So we just stayed with it and dropped him on the right and it still worked.
The issue people dont realise is just because you are fireteam leader doesnt mean you are host of the current game. you need to be on the map on your own then invite your friends and when you want to try again Do Not just invite the host back in and promote him you have to get the host in a game on his own and invite everyone to try again.