Just a resource possibly

[Dale E]

https://www.partshotlines.com/ Type in the car information you want to look up and it will search for a listing of parts you select in the salvage yards around the country. There are a lot of 2.2 Cobalt engines. You can use this for any of your cars. Maybe there is a bargain in there somewhere.

And I let another 2.2 automatic Cobalt go at police impound for 495$..

 

[Vwsaabvt]

car-part.com seem to have a little more user friendly layout, not sure if you have used that one before.