The fic has some serious flaws (such as the author not actually understanding basic screenwriting techniques) but it's overall pretty well-written, with an interesting story, naturalistic character evolution (yes, Shinji and Asuka are eventually shipped, but it comes off in an unforced manner to me and Rei isn't abandoned or marginalized — quite the opposite), and some excellent production values. Also, while Lyn might seem like a boring, unnecessarily close to Shinji addition to the cast, Aoi is a unique character who's just as interesting as the original cast (in my opinion). Tenkei's got his moments too. Worst parts? The bad formatting, slow beginning, and dull characterization of Lyn for much of the series. Best parts? That the canon characters seem like themselves (with a few exceptions), the ending is fairly satisfying, and the other O Cs besides Lyn are pretty interesting.
Overall, I'd say that Eva-R is worth a read, but isn't the best in terms of being a coherent way to expand the canon story. Where it definitely succeeds is in making the reader care about the new characters, their stories, and their interactions with the canon cast. I also liked the script format, but it could stand to have some tweaking in terms of how lines are written and where some setting descriptions fall in relation to the related dialogue. The artwork bounces back and forth between almost as good as the original and very amateurish; I didn't pay any attention to the music or other content.