Despite all of the swearing, violence, and mature content...

Not just a Disney movie. Just any normal kids film. They all use the same general plot, with just different characters. I saw something about the making of the movie where Matt and Trey had to go to a scriptwriting class to learn how to write a full length movie script. The class pretty much taught them what every kids movie's plot is. Add violence, profanity, and the boys, and you have yourself Bigger Longer and Uncut!

I do think they had Disney in mind, at least somewhat. The movie's actually sort of consciously an anti-Disney movie (crude, stiff animation vs. lush, fluid animation, swearing and violence vs. family friendliness, realism vs. fantasy). The music does seems like it's a take on Disney.

The elements you listed could be partly a send-up of Disney, but I think most of that is stuff they did in the series anyways or general "big movie" concepts they used (sort of satirically) because it's supposed to be a "big movie."

they did, it is actually a parody of Disney movies. They wanted it to be epic in contrast to what the show looked like (then, it was really trashy and underground). You are right for what concerns the opening song, but also think about "up there" which is a spoof of two songs with very similar concept in "Little Mermaid" and "The Huchback of Notre-Dame". I do believe it is an affectionate parody and much of the strenght of the film comes from a solid script based on the classic "hero jounrney" template on which Disney movies are based too.