Well, by rough I mean she's very much a tomboy. She doesn't like to show her vulnerable side much. Having grown up around a number of tomboys, I've seen how difficult it is for them to walk that fine line between being "girlie" or not being seen as a girl at all. The character designer for Sayaka even mentions how she felt maybe Sayaka looked too much like a boy, so she added the angled haircut to give her some feminine appeal.
I do think, that in a world without Kyubey, all of the girls could have been good friends. One of the time lines even alludes to such an outcome. Sayaka may be difficult sometimes, but as you point out her loyalty in friendship is a rare thing to see. She's a White Knight persona in my eyes, the "prince" who tries to do the right thing, fight for justice, be loyal to friends, love deeply, and protect what she treasures. It's also why I agree with Homura, who speaks from experience and prior knowledge, when she says Sayaka isn't fit to be a Magical Girl. Thanks to Kyubey, good intentions lead you to hell.
Overall, I pretty much agree with what you're saying.
