Graphics Card Failure
Given that Apple was offering free replacements, my recommendation is to go to a physical Apple store location and ask for a replacement. Apple still services these machines, and will be willing to quote you a price for replacement. There's a good chance that they'll offer to replace it for free given the circumstances, though the fee is up to their discretion.

Failing that, you could replace the GPU yourself. The GPU is an MXM board slotted into the logic board; while it's not the easiest thing to repair, it is serviceable. 



Unusually, iFixit doesn't have a full repair guide for this model, but the limited guide should be enough to get you most of the way there. A 6970M or 6770M should work.