What is the oil change history? Even with the timing off the car should not burn oil? I would start by pulling the injectors and getting them checked out. That is simple and cheap. Then I would find out how to time these things and do it myself or probably have the dealer do it.

Did this happen all at once or over a period of time?

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2016 Corvette Stingray 2LT
1969 280SE
2023 Ram 1500
2007 Tiara 3200