When I taught "Gatsby", I did so in a Language & Rhetoric course. Instead of doing the standard New Critical Theory thing, we evaluated the statements Nick presents as factual, particularly those he makes about himself and about Gatsby, with the larger goal of 1) building a broader understanding of character as it relates to language and the presentation of the self, and 2) looking for inconsistencies (the end of Ch. 3, for example: "Everyone is guilty of at least one of the cardinal virtues, and this is mine. I am one of the most honest men I know." (paraphrased slightly)).
I can't speak conclusively to whether or not this was the best possible approach, but I will say that I had more than 30 students (out of just over 120) come up to me and say "Mr. E, this is the best book we've ever read in an English class." I'll also say that class discussions were livelier and better informed than any of the college literature courses I took (students were required to use quotations to back up almost every evaluative statement they made, and by the end of the 3-4 weeks we spent on "Gatsby" knew the book almost as well as I did. I cannot say the same for even my senior/grad level literature courses in college).