If the buy back is easy, just do that and start over. If they make it a pain to do a buyback get a new engine and then like others have said argue depreciation loss/extended warranty coverage. You will now have a vehicle that doesn't have it's original engine (that matters to some people). Did the dealer give you an ETA on repair time? I'd imagine it's going to take awhile until it's back up and running again. I'd fight for as many things as you can get.
My lady went threw 2 years of issues with her last Subaru (multiple electrical issues). She barely got to drive it because it was at the dealer so much. While she didn't get a buy out "officially" the dealer and Subaru between them "bought" it back as long as she was willing to get a new Subaru from them. They kept the payments the same, gave her a killer interest rate, free 8 year bumper to bumper warranty, plus tons of other extras at their cost or free. She was kind and had patience, and in turn the dealer/Subaru was very generous with what they offered back. Point being I'm sure this would be frustrating, I know I'd be upset, but take a deep breath and push threw it. I find being kind to people usually gets me farther than being an ass.
I'm sure it will all work out for you. Good luck!