Personally, if I were writing a girl!Harry fic, I would significantly alter her relationship with the Dursleys, and through that her views on the magical world. Let's call this theoretical character Daisy, in order to distinguish her from other female versions of Harry.

Petunia does see more of Lily in Daisy than she does in Harry; however, instead of outright rejecting her, she sees Daisy as a version of Lily that can still be saved. So on one hand, she would be more "loving" towards Daisy, but on the other, Daisy would still be harshly punished for any accidental magic. For Daisy, the punishments would be more traumatic; unlike Harry, she wants to please the Dursleys, and it's the rejection that really hurts. Instead of being thrilled by the magical world, she hates it - she wishes she was normal, so her family would love her. At the same time, she's desperate to please those around her, and the magical world is all she's got.

Overall, she'd be less of a rebel than Harry. I doubt she'd make Gryffindor, though if you wanted to keep the same cast you could make an argument for it. Nor, however, would she be in Slytherin, like in other AU fics; Slytherin is overly proud of its magical lineage, and Daisy would loathe that aspect of them. Instead, I think she'd fit better in Hufflepuff. At first, she just wants to be accepted by anyone and will do anything to fit in, but eventually she learns the meaning of true acceptance and loyalty.

The main issue with such a character, story-wise, is that I think Daisy would basically start out as a less intelligent version of Hermione, almost painfully afraid of breaking the rules. And unlike Hermione, who gets kind of dragged into things by Harry and Ron at first, she'd have no motivation to get involved in the plot. Plus, I think GoF and OotP would leave her traumatized and depressed - not exactly a character arc I'd enjoy writing.

Note that, I don't think this is necessarily specific to a female Harry; a similar AU could be done with a male version. In fact, this goes so significantly beyond making him a girl that gender would be incidental to the plotline. However, as far as using a genderbend to take dramatic liberties with characterization goes, I think this is more reasonable than a naked ninja-druid sociopath.

I think it can be done well, but it seems like the differences here are a bit stereotypical? There doesn't seem to be a reason why a Harriet would necessarily be friendlier or be worse at Quidditch. Though since you are exaggerating I guess it makes sense?

I think she'd probably have a different experience of being bullied, though.

Also, on the Snape thing: I once saw someone say on Tumblr: "If Harry had been a girl Snape would have treated her the way Petyr Baelish treats Sansa Stark."

Sybill Trelawney's prophecy.

"...and the Dark Lord will mark him as his equal..."

Meaning this: Voldemort knows that the boy who's going to kill him is just that--a boy.

Which means that Neville Longbottom's parents are killed, Neville takes over Harry's role (and does things very differently, because Neville is a very different person from Harry).

Harriet Potter goes on her own way--no scar, no fragment of Voldemort in her. Maybe her parents still die, because let's face it, Lily and James Potter would've been Voldemort's enemies regardless of whether they had a boy or a girl.

It changes literally everything about her life for her not to be the Girl Who Lived. Not that she wouldn't get herself into trouble anyhow...

The hard part would be making Harriet Potter different enough to not just be a rewrite, but also similar enough that you don't warp canon. If this can be accomplished, than I'd go for it. If it can't be accomplished, than I'd still go for it, just maybe write a few short chapters, as anything else is not really worth your time. I like point number six that you came up with, as that could make for some interesting bits.

Should it be done, now, that's the question. When doing gender bent stories, you often run into one major problem: blatant plagiarism. Oh, yes, there would be some differences, but on the whole, there is not enough difference between Harry and Harriet to warrant a full fic, ala Rose Potter. Now, a one-shot AU? Possibly. Multiverse hijinks? Entirely probable. Tumblr ask blog? YOU BET! Rake in those reblogs. But full, multi-chapter fic by itself? I just don't see it working.

That all said, I do like the analysis you made on the difference between Harry and Harriet. I am a little hesitant on the Parseltongue aspect of her, but on the whole, I can get behind this.