H3 needed new engine ALREADY?

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My dealer must be doing something wrong. I stop by and have coffee and they are dead in service. However, if a dealer is busy and all qualified techs are working then it is on a first come first serve basis. This is the same at any dealer, and any manufacturer. Not all techs in each dealer are qualified to diagnose an engine problem. Some techs will be only trim/radio/seats, etc., and some will only be heavy repair such as trans/engine/axles/etc.
However, this is a known defect and has a bulletin issued. Idles rough, code P0300-5, fails test and a new head should be ordered immediately.
As for taking to another dealer. I guess no one has tried to take a Vette into a Pontiac dealer for service, or a Cadillac into a Chevy dealer for service. You will be asked to take it to the proper dealer, unless it is a major repair the dealer can perform.
For the cylinder head issue, not all GM dealers have the correct special tool to perform the repair. Off the top of my head, only Hummer/Chevy or GMC would have this tool.