I wonder if Galadriel was still in Doriath when Turin lived there

Good work Brethil.

I'll look at things more generally and from another angle: if we take the constructed Silmarillion out and look at the Quenta Silmarillion in HME, Galadriel sort of 'disappears' after a while. According to The Lord of the Rings, Galadriel appears to have passed over the Blue Mountains before the fall of Nargothrond ['ere the Fall of Nargothrond' and so on], and met Celeborn in Lorien, but the mountains are not actually named, and by the time of the Appendices at least, Celeborn became Sindarin [not Nandorin] too.

That said, Christopher Tolkien refers to an interesting statement about Celeborn in Unfinished Tales: 'It is a natural assumption that Celeborn and Galadriel were present at the ruin of Doriath (it is said in one place that Celeborn 'escaped the sack of Doriath') and perhaps aided the escape of Elwing to the Havens of Sirion with the Silmaril -- but this is nowhere stated.'

That probably doesn't help though She really does disappear for about 350 years or so. Actually this does help Elthir - with placing Celeborn and Galadriel at Doriath as a 'natural assumption' it seems to suggest continuity of that (if nothing else including versions of Celeborn - at least he isn't Teleporno anymore, thankfully) place as a central spot for Galadriel. So we have the early visit to Nargothrond as a stated exception, but with this bit from CT placing them at the sack of Doriath it does seem presumptive/negative inference that, if she isn't actually said to be anywhere else, that is where she would be. Thanks!

(...) So we have the early visit to Nargothrond as a stated exception, but with this bit from CT placing them at the sack of Doriath it does seem presumptive/negative inference that, if she isn't actually said to be anywhere else, that is where she would be. Thanks!

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I think this represents the 'later history' [if not the ultimate version, considering the very very late 'unstained Galadriel' version], and to my mind, in this phase in makes sense that both Galadriel and Celeborn remained in Beleriand, and so why not Doriath, until its fall.

That's how I imagine things anyway, and essentially I force Galadriel to mean different mountains [mountains in Beleriand, not the Blue Mountains] when in The Lord of the Rings she seems to speak of passing 'mountains' before she meets Celeborn.

That's how I make it 'work' even though I admit my idea is a bit awkward. Of course Tolkien wasn't done tinkering with Galadriel as a banned leader of the Exiles, despite what he published in the 1960s...
... but that's another tale

Perhaps the difference was of recognition of their ambition?
I don't see Feanor as introspective at all. The quick pace of the Sil might contribute to this conception, but he seems to do something, and burn all his bridges (or boats) behind him. He doesn't seem like a planner, more of a revolutionary. Strong, powerful, successful...... remind me..... what the mortality rates for revolutionaries are? That's very true Rem, and even when Feanor is born he is recognized as having an inner fire that burns perhaps a bit too bright. Galadriel lives and functions within the confines of the larger world, where Feanor really tries to remake the world around his desires. And yes, you are quite right: the odds are not so good are they?

Galadriel OTOH, really seems like a power under control. She can let loose, but chooses not to. I get the impression that she pondered long on her plans, and in one version she crafted a vessel to bear her separately to Beleriand. A lot of planning was involved I think. Thus, she might have been as ambitious, but in her planning she found some measure of wisdom She waited, if only to perfect her designs. Patience would seem to be a very Elvish virtue. When tempted by the Ring, she was in danger of losing that control she had built up, but restrained herself, and by doing so conquered the quick temper that may have been the cause of her trouble with the Rules.
Maybe that is why she was allowed to return to Aman? Because she had proven able to control herself, and channeled her ambition into good ends? JRRT seems to link her reprieve directly to her work against Sauron and her rejection of the Ring. In the passage from Letter # 297 that I quoted upthread, it continues to say (after her prayer for Frodo) "Her prayer was granted - but also her personal ban was lifted, in reward for her services against Sauron, and above all for her rejection of the temptation to take the Ring when offered to her. So at the end we see her taking ship." So the rejection of the Ring at the Mirror is really a litmus test - one that she is not aware of at the time (which legitimizes it morally, I think - in her mind no self-service could be gained by the rejection.) Can we say the sum total of her life to date all comes into play in that one act, because it indicates the state of her spirit in the quest for Power (and therefore the usurpation of Eru)? Maybe!

Since that's what's said in LOTR, I personally feel that's what I have to make fit, not an isolated note briefly mentioned in Unfinished Tales. While I think it would have been cool if Galadriel and Celeborn had been worked into the narrative of Doriath's fall and the havens at Sirion, I also almost like it better that they're not worked into every major event from the First Age. It would feel a little forced in my opinion.

Anyway, this is what I kind of imagine. After her visit to Nargothrond, she probably felt again that desire to rule her own land, and seeing her brother as the ruler of his own kingdom, she probably departed from Doriath sometime in the middle of the First Age. So I think it's unlikely that she was still dwelling there when Turin was being raised. Honestly, that's probably why she survived so long

Unfortunately, I don't have any of my books with me at the moment, so I can't check all the references. But I think this is the most likely course of action.

Hmm... There seemed to be done kind of enmity between Galadriel and the Valar, the reason she 'needed' a pardon. This unwitting moral testing might have been used by Eru/the Valar as a final gauge of her moral center. They did not orchestrate the test, but in seeing the results, they could commend her resolve and know she was good at heart.

One last point - in The Road Goes Ever On (which I haven't read yet), Celeborn and Galadriel are supossed to have remained in Beleriand until Morgoth was defeated.