Thanks everyone. It's very interesting reading all of your opinions on desensitizing. I am inexperienced, but learning. I've started working with my trainer, who was highly recommended by several horse people I've talked to in the area, and she says she's never seen a horse act like he does before. We're doing what some of you had suggested, going back to basics. Working hard on respect and small steps, and treating him like he doesn't know anything at all. She thinks part of the problem is he never had any formal training when he was younger, and now that he's 9, it's harder to break some of his bad habits.
As for the person who asked how I responded to his spooking, I don't coddle him, but I also didn't make scarier either, because I don't think he knows any better right now. I tried just walking around the arena with the blanket, shaking it, flinging it around, like it was something I did every day, until I peaked his curiosity. I'd have him follow it, to build his confidence, then have him stand on a lead line and shake it around until he relaxed and seemed comfortable with it, then moved it closer and closer until I could touch him with it. He never calmed down when it was touching him, but he didn't run from it, which was improvement from where we started. I like my trainer a lot, and I feel like we've made a couple of tiny breakthroughs already, so hopefully she can help me continue to figure him out. Thanks so much!