Wow, it looks like since I posted this question, the Teschl notes linked by Alexander Moll have in fact become an AMS GSM, so maybe that's what I was looking for.

Thank you for the comments! I would prefer something in print and for grad students, though. Arnold's book is beautiful, but I find it frustrating that he sweeps important things under the rug so that the exposition goes smoothly. I would like a book that is completely honest about everything. I want to learn about ODEs thoroughly, for their own sake. I am interested in relations to other areas of math; I am indifferent to physical applications. My ideal book could probably be published as a GTM from Springer or the AMS. Is this helpful? Thank you!