You are asking some very good questions.
A couple of thoughts:
Contact the Los Angeles Economic Development Office (see link below).
Select a manageable sample size of charter/magnet schools, Google the school name and Real Estate and see what comes up. I would talk with the Realtors that work near those schools and see what you can learn.
I can tell you that school test score definitely are important to buyers. There might be a correlation between school test scores and home values, although i do not know where that information might be. LADEC might have data on that.
IN the markets I work there are four different school districts, and I can say without a doubt that school quality has a major impact on not only home values, but also home value stability. However, these area also have other aspects that affect value (separate cities, like Glendale and Burbank, LA County, and then LA City). The services provided by these entities to residents also make a significant impact.
So for your analysis I would focus on schools near by and talk with local Realtors.
Good luck. Send me a copy!