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Is the egnine in the car? I'd focus on that first. I have a 2013 CTS with the 3.6, so of course I looked into this swap a few years ago, and found on various forums that most of the drivetrain components are different between CTS and CTS-V, like the front crossmember. I see you have a photo of the Pure Fabrication crossmember. https://www.purefabricationllc.com/p...bular-k-member
Are you using that one? Or find a stock CTS-V crossmember. Or I guess go old-school and fab up mounts to put the LS2 on your CTS crossmember, but I think I would take advantage of the GM engineering. I don't know if you'll need a new transmission crossmember, but I suspect so. Maybe use the GM one.
Once you get the engine and trans in, you'll need to deal with stuff like driveshaft, exhaust, radiator, trans cooler, shift linkage, bigger fuel pump, and other details.
I think you could use the stock CTS-V engine harness. You might have a few differences between your engine and the CTS-V. I don't know if the PCM is the same for the 3.6 and the 6.2; you'd need it flashed at least, or a new PCM. Not sure if that would be sufficient for all the gauges to work, but theoretically yes. Don't these cars have BCMs that need to be CTS-V specific?
I think I'd approach it with more of a swap mentality. Use an aftermarket harness, get it running, find some solution for gauges, and drive it. Don't bother with any integration between the dashboard and the engine.