I have the exact same issue, and my Apple Care just expired a couple months ago. Does anyone know if I am still eligible for a replacement?
They replaced the display for free outside of AppleCare. I didn't have to argue with them at all, so I suspect that this is their standard response. YMMV if you have a newer model.
However, for the OP, don't let this stop you. Call and ask, they often are generous enough to replace it for you even out of warranty. If the first time doesn't work out, try again 2-3 more times before giving up.
The AppleCare for my 2012 rMBP has expired, but is it normal for an Apple store to be so stingy about repair extension programs?