I had the same problem. Personally, I was using model glue to stick em back on. Took a few attempts, and had to basically hold the wings in place while the glue dried. Took around 30 minutes to get it done, but at least I didn't get any of the stuff...
I second the music, and the anime series was relaxing and enjoyable to watch, kind of like Aria Sadly, I have yet to check out the comics...I will have to add it to my list of things to do.