If anyone is still following this post, I've gotten nowhere with this issue. I took my Cobalt to a very reputable transmission shop this past Friday. He kept the car for two days and had another knowledgeable mechanic look into it. Both are ASE certified and have 70 years experience between them. They could find nothing. Took it to the Chevy dealership. They drove it and checked the ECM and TCM. Could find nothing. The mechanic told me that he has seen this in other models and that doing a fuel injector clean and top cylinder clean with new plugs would make it better. I did a top end clean with Seafoam, replaced the plugs with OE plugs and rather than clean the injectors, I've ordered new OE injectors. So far nothing has helped. Hoping injectors do it.
To recap: I've changed the oil and filter, new air filter, new fuel filter, new AC Delco plugs, top cylinder clean. Had a tranny shop run diagnostics on tranny and engine, and I am waiting on injectors.