I was given this controller for free because a trigger didn't work. After taking it apart I quickly saw that the board was actually cracked under the analog stick. I removed the stick and the board just fell in two. I decided to see if I could repair it just for fun! I know its much quicker and cheaper to just replace it but sometimes you have to address that "what if?" question.
I started by gluing the two pieces back together using super glue then two part epoxy to really hold it. Once the boards were whole again I started the repair process which consisted of manually reconnecting all the traces that were broken with the board being cracked in two. To do this I had to scrape away enough solder mask to expose the copper underneath, from there I was able to apply solder to the traces and use 30 gauge wire to reconnect them.
For some reason I find this incredibly enjoyable and the fun I got from managing the wire bends and fine soldering was worth it.
I assume that there are more then 2 layers, but were you able to make it work again?