I got all three exotic swords on my warlock. Dunno if you're doing this already, but Lost to Light is a great level to get the kills. Once you get to where you can pick up the relics, pick one up once your melee is charged.
With the relic equipped, your melee will never deplete and every kill you get with the relic will be an ability kill, thus counting toward the quest.
The second and third rooms are good and have a lot of enemies. I think the second room has more enemies. The poor part is that each room has its own checkpoint once you open the doors. So you'd want to figure out which room you like the most, and when you've killed everything in the room, just jump off a nearby cliff.
This works for any class and subclass. If I had worked on a Defender Titan instead, I'd do this strategy exclusively.
