
Now that the exclusive limited omfg rewards for remnants are available, what are some of the ways to farm them?
Personally, I've had most luck with dual boxing part 1 of heroic elite Devil Assault with a lvl 18 (or less) character. Between 5-8 champion chests, and 1-3 remnant drops, I can get 50~100 or more remnants per run. I recommend fighting at the portal opposite the door to minimize the underground chests - or rather, some chests still spawn underground, but they usually can be opened. Hireling helps keeping the dualbox alive and also makes looting of the chests easier (particularly if you're pooling remnants to a single account.
Another interesting tidbit: Anyone can pick up champion droppings, regardless of level, presence in-quest, etc. If you have a quest with a small map and a bunch of remnants on the floor, you can bring in your dual box (or guildies... duh) to pick them up, even after the quest is complete. You can also have your dualbox / guildie keep the completed instance active, log on a different character(s), and pick up everything again. And again. For example, you run the entire DA, have someone hold instance and collect those remnants on various characters (DA: small map, lot of mobs, lot of champs, and also accessible to wide level range).