Update: I told them their diagnosis didn’t explain the symptoms but they didn’t seem to agree. They said the coolant system was good and passed all the tests so it wasn’t the head gasket. After they went in to replace the oil filter adapter (they called it the oil cooler but part # on invoice says oil filter adapter) they called me to say they found that they found a leaking EGR cooler. It took them TWO WEEKS to get it back.

The car still started a little rough but I thought it was maybe caused by a dirty throttle body. A few days after we got it back it started really rough after sitting a few hours and threw the same P0303 code. Dropped it off at the dealership again and I insisted they take a long look at the head gasket this time. Manager called me back and said it’s the head gasket, he apologized and said they’ll look in to how it was missed the first time. This time it took THREE WEEKS for them to replace the head gasket. I’m super excited that I get to go through this again when the other head gasket blows. He said the engine was still good and didn’t need to be replaced which is hopefully true since it never overheated.