The problem was that the project in Advanced Installer was configured to compress the JARs included with Pack200, and this was breaking the digital signature of a part of those JARs.
The solution is to either disable completely Pack200 compression or to go to "main application menu -> Options -> External Tools" in Advanced Installer and in the dialog that appears specify the installation path of the JDK you are targeting from your application. (This last method will allow Advanced Installer to check the digital signature of the compressed JARs, detect which signature is broken and automatically skip those JARs from compression, BUT still compress the other contents of your package).