Rough idle on a 2005 Chevy Express 1500 4.3 V-6

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Problem with the Chevrolet Express 2005 Express. Rough idle on a 2005 Chevy Express 1500 4.3 V-6. At cold start everything runs great until I shut it off and wait 10 minutes then when I restart it runs badly coughing and sputtering and almost stalls out. I can nurse it along for about 5 minutes and then it clears up and runs fine. I was getting a PO430 so I replaced the cat on bank 2 but that solved nothing except I no longer get the PO430 code. Now I am getting a PO300. The strangest thing is that it clears up after about 5 minutes and runs fine. However, the other day I left it idling for about 10 minutes and it started its misfire problem again but only worse. It took about 20 minutes to get it to clear up that time. I took it to a local mechanic shop and they are stumped. Thank you in advance for any suggestions!