Mac-Mini 2011 - AMD Radeon GPU Failure

Hello everyone, I meet with my mini 2011 (AMD video card) the same problem as the MacBook and iMac to the same generation. Apple has launched an extended warranty for Imac:

iMac (27-inch): AMD Radeon 6970M Video Card Replacement Program - Apple Support

macbook :

http://www.macrumors.com/2015/02/19/2011-macbook-pro-repair-program-apple/

But nothing for the mini that has exactly the same problem. There are other mini users who have had problems:

https://discussions.apple.com/thread/7436149?searchText=2011%20AMD

Mac mini mid 2011 display issue AMD radeon 6630m

And many others I'm sure.

I know he is selling fewer mini but that does not excuse either. I return from GeniusBar that tells me that this has nothing to do. And presents me a motherboard change quote the price of a new mini. I grant that it takes to Apple supports this as repair for MacBook and iMac to the same generation with an AMD video? I am taking advice and opinions. Thank you for your help.