I left her quests for Ultimate to get highest reward (and to stock up on Black Legion augments beforehand). They are not super interesting, but challenging nonetheless. Got a mythical relic blueprint for one of the quests. Lore is semi-interesting too.
Just wait till Ultimate, then do all of her quests before Gates of Necropolis/Immolation quests Black Legion (main storyline) quests. Then do those remaining story quests. Reputation problem solved, everyone’s happy.
You can always go back to do the challenge quests in the various difficulty levels, for ex if you’re not geared enough or don’t have enough resists, doing the last 3 quests for Anasteria are fairly hard.
I’m not familiar with how the difficulties work yet. Does this mean you can only do them once in total? Or can you do them once per difficulty?
Can you switch freely between difficulties (for some reason), or do you have to stay in Elite once you’re done with Normal/Veteran?
Ok, now I see how the five quests are set up. The first two are pretty straightforward, but the last three involve the rogue-like dungeons. I already accepted the third one, and it will annoy me to no end to leave it open in my quest log, so unless I can abandon it for later, I’m going to have to do it to appease my OCD. 
After that, I suppose I’ll just stick to killing mobs for rep.
What happens if I still have one of Anasteria’s quests (or any bounty) in my log when I switch difficulties?
Nothing in particular. If you go back to that difficulty it will still be there, but it won’t show up in the new difficulty. Not sure what would happen if you have the same quest in multiple difficulties as I’ve never tried that, but I would assume it would not be an issue (I imagine I’d have seen complaints about it if it was a problem.)
Ah, thanks. I didn’t realize they were kept separate like that. I just beat the last boss so I’m about to switch to Elite and see how that goes.
As an aside, I wasn’t quite expecting the game to end there. That didn’t seem like the most pressing threat or storyline that the game was building up to. It seems incomplete, unless higher difficulties actually add more to the story?
Each difficulty is basically a separate instance of the game. If you have the same quest in multiple difficulties, completing in one difficulty will not affect the others at all.
Great to know, thank you!