Look, if the shop failed to notice something that they should have, that's on them. Screwing yourself over for someone else's error is just plain silly, no matter how much work you've had done through them. In fact, if their inspection work is that shoddy, you're better off finding a different shop, anyhow.
Secondly ... was the car sold-as is? If so, the BUYER is screwed, not you. You're not a dealership, are you? And even if you were, you're past the usual 30 or 90 days allotted in most areas for people to report car issues, unless the "warranty period" extends to a full year or there was a written warranty or agreement signed and given at the time of purchase.
I guess I'm missing something of the background story here, because this really all just doesn't make sense to me why a car sold on September should be your responsibility in January of the following year...