I'm also having this problem with a 2013 Grand Sport with the 60th Anniversary 4LT package.  I've been told by a reliable upholstery shop that my options are to remove the dash or remove the windshield and repair it from the front.  The second option seems more favorable as I'm concerned removing the dash could create electronic gremlins of rattles.  The danger with removing the windshield is that it could crack in the process.  Did you address the issue on yours?

This is a problem mainly with the 4LT packages. I look at mine all the time but so far so good. However I have a couple buddy's who have this problem with their 4LT C6's. It is a factory install problem or so I've been told. GM did not give them any options when they were contacted about this. Sorry to hear you have this, not an easy or affordable fix.