Never had any issue to complete this, did it over 10 times. BUT: run 1 sword at the time, don't try to "win" time by doing several, you will fail and end up loosing more time ... So 1 sword/player at the time. Example: you need the solar exotic sword? Equip your legendary exotic sword at the boss encounter. Kill the 2 Knights you don't need (arc/void), do NOT damage the solar knight as if a thrall explodes next to him he can get killed. Once 2 knights down, do the strike as usual just leaving the last knight untouched. Once the Darkblade is very very low health, ask your fireteam to not damage the boss or the knight anymore. The one that need his swords takes his legendary sword and kills first the Knight, than the Darkblade. Don't think the sword is needed to kill them but I do it ust ot be sure. Works every single time.

Try doing it one knight at a time, killing both the knight and Alak-Hul with the appropriate sword?

I was part of this fireteam. This isn't a matter of skill, as we have the light level required and then some. We have killed the boss and then the knights within 30 seconds, killed the knights and then the boss in 30 seconds, killed just the required knight for the specific sword we are using and then the boss and vice versa. Literally every route has been explored and done easily within 30 seconds. I have the void sword and it says i've killed Heolstar, warden of Oryx but Alak-Hul is greyed out?