Corvette exhaust back pressure sensor issue

I had a similar issue with my Corvette, albeit I am unfamiliar with the specifics of the 2005 model year. The symptoms you describe strongly suggest a problem within the exhaust system, possibly related to the exhaust back pressure sensor. The sensor's role is to measure the pressure in the exhaust manifold. This informs the engine control unit (ECU) about engine load. Before condemning the sensor, have you inspected the wiring and connectors associated with the sensor?

Wiring looks okay at a glance. What sort of readings were you getting when your sensor went bad?

In my case, the readings were erratic, fluctuating wildly even at idle. Given that you've observed smoke upon acceleration and a warning indicator, it is probable the sensor is defective, leading to incorrect feedback to the ECU and subsequently, abnormal combustion. While further diagnostics could pinpoint the issue with certainty, the symptoms are strongly indicative. I would advise consulting a certified mechanic for a comprehensive evaluation and potential sensor replacement.

Thanks. Took it to the shop; you were spot on. Exhaust back pressure sensor was indeed defective. 245€ later, all sorted.