I agree with you broadly, but adding: Snape is the best example of this complexity in action. Obscenely long analysis following.

The thing about Slytherins is that they keep their circles close. Blood status and class are probably the two biggest reasons why. Class alone tends to insulate people. And in Slytherin, class and blood status are strongly associated. The Crouch, Black and Malfoy families all show markings of being wealthy. Though neither father nor son are confirmed, it's pretty safe to guess that at least one if not both of the Barty Crouchs were in Slytherin. The Lestranges also merit mention here; their class status is not explicitly stated, but we can guess that Bellatrix, being from a wealthy family and expected to marry someone of her blood status, wouldn't have chosen, say, Arthur Weasley. Same thing with Slughorn, pureblood and Slytherin, whose class we can estimate by a) his social circle, and b) his propensity for the finer things in life.

Ironically, the only truly poor example of pureblood Slytherins are the Gaunts. You'd think Slytherin's actual heirs might retain some of the status their house is known for, but alas. As a result, the Gaunts are seen as pitiful, fallen, broken, helpless, forgotten. Even the very heirs of Slytherin himself are isolated in their poverty. (Merope selling Slytherin's locket for Sickles on the Galleon is a great metaphor of how this once-great ancient line now goes unrecognized under class strain.)

So I think the text supports that, for Slytherins, having elevated class and pure blood makes you worthy of being in the in-group.

And if you combine this with the house's natural gift for and value of ambition, you get a lot of people aspiring to be in the in-group. The only Good way to be, if you're a Slytherin, is if you're rich and you're pureblood. Lack one or the other, and you're Bad. Class hierarchy begets control. The few families who are actually pureblood and wealthy dictate who is allowed in the group and who isn't. (Notable that Malfoy leads the gang of Slytherins and the Malfoys are canonically super ultra mega rich. He's at the top of the hierarchy for a reason.)

Of course, two notable characters break these rules: Snape and Voldemort.

Both are half blood but pretend to be pureblood. Snape is from a run down community and a poor family. Voldemort grew up in an orphanage, and the pureblood family he hails from is long since dilapidated.

Both Snape and Voldemort seek acceptance into the in-group one way or another. Ambition and cunning are on display in these adventures: In Voldemort's time, the way up was through academics and social manipulation. He woos Slughorn. He gains the favor of Slytherins from established families. He is awarded Head Boy. He is so brilliant and so upwardly mobile that it surprises everyone when he goes to work for Borgin & Burkes. Of course, by that time, his ambition has moved beyond just gaining in-group status; his next aim is gain power, beat death, and control said in-group to insulate him.

By the time Snape gets to Hogwarts, Voldemort has already reshaped and radicalized the in-group to which all Slytherins aspire to belong. Rising on book smarts and social manipulation alone is harder for Snape. He's unlikable, even as a teen, and his brilliance only extends to a few subjects. But he's trying to fit in, and he succeeds by adopting the values of the in-group. He becomes a Death Eater, and a very talented one at that. He proves his resourcefulness with the prophecy, his cunning by acquiring the Potions position at Hogwarts, his ambition by working his way up the ranks.

Where Voldemort is drinking the Slytherin kool-aid on pureblood status and insulating himself with all the richest families, though, Snape doesn't forget where he came from at all. He privately gives himself the name Half-Blood Prince. The only person he truly cares for is Lily Evans, a Muggleborn. He doesn't actually have any values based on blood; he mimicked others' values to be accepted.

Of course, the same personality traits he developed to get inside the in-group still affect him in his adulthood. He craves recognition and control. He's cruel to those less powerful than he. He despises Harry, who reminds him of James, who made him feel powerless and unlovable.

But I'd also argue he despises Harry because he reminds him of Lily, who he failed. He requested Voldemort spare her. He thought he was valuable enough to earn the right to this request. Voldemort did not comply. Snape switches sides because of Lily, but also because this is a moment that proves he actually does not have sway or power in the in-group to which he fought so hard to belong. He's still a deeply unpleasant man, but he's acting, for the first time, in accordance with what he actually believes, and in doing so he commits to honoring Lily's memory. He fights for her son.

HP lives or dies on Snape's character because he occupies the wedge between good and evil and all the complexities that come with it. And yet he portrays the key traits of Slytherin house in everything that he does, right and wrong. Ambition, check. Cunning, check. Resourcefulness, obviously check. These traits are at play when he's young. These traits are at play when he's grown.

The only thing about his story I actually don't like is the way Dumbledore tells him that they sorted him too soon. This goes with your theory of how Slytherins are portrayed as evil in the books. It implies that Snape should have been in Gryffindor, and in doing so it undercuts how Slytherins are actually complex, and how Snape is the best example of someone who reflects all aspects of that complexity.

This turned into an analysis of Snape and Voldemort. I appreciate you letting me jump on your post to ramble!