This story is so painful to read, and I rarely feel that way even in extremely angsty stories.  It's the juxtaposition of a strongly IC Snape, and this very fragile and fearful Harry.  As to Harry being OOC -- well, putting him in Slytherin automatically tells the reader that he's not strong enough and confident enough to object to the Sorting Hat.  What would it take for canon Harry to be like your Harry?  Probably not a lot.  Probably just a bit more abuse from the Dursleys -- not necessarily major physical abuse, just some.  Dumbledore in canon is right to be amazed at how Harry turned out.  Living in a home where the child is put in a closet for weeks at a time (Harry recalls at least one incidence of this in canon where he goes in while school is in session and doesn't get out until after summer holidays had started), combined with lack of decent nutrition, serious verbal and other emotional abuse, and general neglect, is more likely to produce a child closer to your Harry than to canon Harry. 

So, basically what I'm saying is that your Harry may be OOC, but he still makes sense. 

I hope you can update again especially quickly, because this was a great chapter that just begs for more.  Snape's bitterness is so strong, it colors his perceptions and makes him sometimes blind to what's really going on with Harry.  I'm looking forward to finding out what he does next.

 Also, I like the way you show Harry having strong potions ability (which Snape seems unable to admit that he could have got from a parent).  And I like the way you show the difference in an intuitive ability in potions, and Hermione's "by the book" approach.

Once again, great chapter.

I know you said you started this as a one-shot (I think), but at this point, how far do you think you'd go?  Since you're getting into plot twists with Quirrell it sounds like you'll tackle the whole Philosopher's Stone book.  Which I think you could do with this Harry, given some growth in him.  And it would be very, very interesting to see Snape's perspective in that.

 But if you want to do that, I think you'll have to expand the number of characters Harry relates with.  Another reviewer mentioned Dumbledore.  I agree that's an issue.  I can't help, but wonder how Dumbledore would relate to Harry in Slytherin, and particularly Harry having this degree of "damage" from his abusive home.  Personally, I'm not into "bad Dumbledore" perspectives, although he does seem biased toward Gryffindor.  On the other hand, there's a sense in which his primary bias in the books is toward Harry specifically, and Gryffindor as a result of that. 
Anyway, will you bring Dumbledore into the story? 

And then there's other students and Hagrid.  I guess what I'm really getting at is that even if you decided to take Harry through the events of PS/SS with a somewhat different mix of friends, he'd still need to expand the group of people he interacted with.  And of course that brings up Snape and how Snape is relating to Harry and how Snape would relate to others that might enter Harry's experiences, such as Dumbledore or other students.

 I'm looking forward to see where you take this.  I like your writing.  Each chapter has been quite satisfying!

Wow!  Excellent chapter.  You move the plot well forward, while pulling Snape into this growing commitment to Harry.  The hug and all its implications were so well done.  Thanks for updating this story!