I have fixed a few of these engines in my time. $11k is a pretty high cost for that job but I can see a dealer charging that. The cost of a head plus all the extras to fit.
Somewhere nearer to $5k if you dont have to go with brand new audi parts.
I dont fancy your chances at Audi unless you had it from new and never serviced it anywhere else. And even then, I'd not expect them to cover the whole bill.
I think you could burn a lot of energy and not get a result, they wont stump up for waterpumps on EA888.3s
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