I wanted to max my Keeper reputation, for completionism, but didn't find any good guides. So, I checked how well the various methods of earning reputation actually worked in practice.

Conclusion:
If you don't care how long this takes (which is reasonable; the only reason to do this is a sense of pride and accomplishment) just run the offshore quest. This has possibly the highest rep/minute even ignoring the bonus Sorm Legion rep, and takes less than 5 minutes a day.

If you want to speed things up further, also do the daily solo and group quests, but skip all quests on the northern peninsula, as it takes too much time to get up there, and run any convenient rifts. (It's really not worth going out of your way for these, but if you're running through a rift, stop and clear it.) Shard switch when needed, and use Planar Attunement teleports to return to quest-givers if you're not near a porticulum. (E.g. teleport to Scarwood Ranch or something, then use the porticulum to go back to Ember Isle.) This should take under 20 minutes, and can be done once a day.

If you want to max your rep in a day, just run rifts until your fingers fall off.

(Underwater rifts, the "Hero's Unrest", and the "Sinister Tide" rifts do not give rep, and Nightmare rifts do not give Keeper rep. Bonus stages do give bonus rep, and should be done. You can open your own rifts from tears, but only use the base "Planar Lure" ability.)

The fishing quest, sourcewell defense, and weekly event quest are not worth doing.


Assumptions:
  • I assume you are leveled enough that level 60 content is trivial.
  • I assume you've done all the regular quests already.
  • I assume you're not doing a speedrun. Times include stopping to pick up artifacts, managing minions, refreshing buffs, and so on, and I'm not hyper-optimizing. I didn't leave the timer going while I made a sandwich or anything, but don't get mad because you can totally do this quest faster.
  • I assume you're doing this solo.

Notes:
Weekly event quest: Ember Isle Events don't really occur anymore...............

Fishing: 300rep, over ~16 minutes. You are gaining progress towards both fishing quests, and it's random, so hard to guess exactly. However, the fishing quest sucks, so I'm not bothering to be more accurate. I ran rare/clever fishing spots, which seem to work better than fishing in open water, but it's still not good enough to bother with. (While the fish can be bought on auction, nobody is selling.) It might be worth turning in a couple if you're also grinding fishing skill or something, but otherwise it's not worth it.

Sourcewell Defence: 245rep over 6:50 (just upgrading everything); 535rep over 14:05 (completing 20 invasions, with the daily quest) This scales with the number of players. Solo is obviously not worth it. A party would be faster, but probably still not great. (Note that each invasion only gives, like, +2 rep; the actual rep gain is from the daily and the +1 spam from upgrading everything.) This may still be interesting if you want the achievement for killing invasions. I tried cycling through shards to manage more than one sourcewell instance, which does work, but is really clunky, and isn't that much better than just doing something else while you wait for new invasions.

Daily group quest: 600rep over 6:42 (fell in the lava and died while attempting to drop down), 4:56, 4:27 (demons in volcano), 3:43 (mermaids), 3:10, 2:41 (dinos in crater).

daily solo quests: 1250rep over 11:53, 13:15, 13:22

daily solo quests, but skipping a northern quest without a good porticulum: 1000rep over 6:01

offshore daily quest: 600rep +100 other rep over 4:17, 3:28 (4 orbs), 3:43, 4:01, 4:41, 3:22 (kill fish). Remember to use teleport to skip the swim back.

rift hunting: 726rep over 6:45, 1140rep over 17:40 (ran a few rifts that didn't give rep), 1007rep over 7:53. This doesn't have a daily limit.

Hybrid method: Basically, run all convenient rifts while you run daily quests. Grab any close rifts or tears while you run quests, and check for anything that's near porticulums whenever you're nearby. 1770rep over 13:57, 1242rep over 10:01, 2569 over 23:01.