I have been dealing with these issues for about 1 year now. Started with cold rough idle and sometimes white smoke on startup. I also had the alternator bracket leak that you will have if not already. I have replaced cams and eccentric shafts immediate levers to spark plugs to DME and coils. Used parts not new, new would cost 2 3 times what the car is worth.

The valve stem seals go bad in these motors, all of them, meaning v8s.
The job to replace them takes a while and I could prob do it in a weekend in my garage. I have had the heads apart in mine probably 5 times now and I am pretty proficient in it, not to my choice though.

It's cheaper to buy a replacement motor however if you try to get one for our age car it will have the same issues. I looked into getting the newer 4.8 which is doable but there could be some issues with harness and if the motor is out of a car you need to swap the oil pump and oil pan etc.

I removed the cats on mine and tricked to post O2 sensors with a defouler. It runs better but still has same issues.

I am at the point of cutting my losses and selling the car as I don't like throwing money away. I have learned a lot though.

Members feel free to chime in but sometimes the turth hurts. I see these V8s in BMW cars all the time and guess what, they are all smoking white smoke out of the tail pipes. It's a shame that an old chevy would last longer than what is supposed to be an upscale, highly technical engineered machine. Then again the did loose the war for this very reason.

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2005 4.4i with sport package