I think farming reaper frags will be a lesson in frustration. I would make it so that the run is worth it for other things as well.
If you are combining it with shard rerolls, then low heroics is the way; then it has to be something quick to get to, repeatable, maybe even one you multibox.
If you are not chest rerolling, them aim for stuff that is quick to get to. If you follow Mornyngstar’s suggestion, Watch Your Step is a fast zerg to the named item chest AND the quest is not done upon looting—so a solo character can hit it 8x. If you do it in heroics, you will get reaper boosted items but they cannot be made into frags (a shame—it is only 1 shard to reroll…but you can try to get a couple reaper 5 rings out of it for heroic ERs, even reaper 5 mythic 3).
Capped characters: 1) Hit Burkat and Snarla chest, WPM. You will get a few K sentient xp even if you don’t get your frags (named items drop in their chest). 2) Bash chest, Blockade Buster—very fast, ship to right, drops armor sometimes)
3) A Frosty Reception—frost giant chest opt
4) If you have a lockpicker—Coin Lord Chest, Eyes of Stone. Very fast.
Heroic farm:
1) Werewolf chest, immortality lessons: drops helm etc, not too bad, cheap (3 shard) reroll
2) Tilomere recommends slave lords; then I would say go for Aerie of the Slave Lords first chest just passed rats
3) Any quest you know well in Saltmarsh or Feywild that you can get to fast. Feywild has the advantage that weapons might drop in them and they could be boosted
4) Tear of Daakan—zerg it hard, lots of junky named items from mini champs along the way (stop at last one—don’t finish the quest. I forget which one is last but you can post it here.)
5) Home of memory—bring pots to skip shrines, cruise to end fight.
6) Redwillows—hit item chests like the Trolls, rinse repeat. Pretty fast.
7) Gwylan’s—like Tear, hit champ chests for various named stuff. You can make it easier by just targeting the above-ground stuff.
8) Irestone inlet—hit Dinks (ogre by shrine) and Skartongue (kobold by entrance). They always spawn, rinse repeat.
9) A frosty reception—run up and kill giant Opt. Not super fast but one more.
Updating…
Best time to do this is Treasure hunt weekends. Not sure how much a pot helps.