Removing the codes means they wouldn't show up again. Clearing is merely clearing and they would be expected to come back
Rereading your first post the car is an 03 with a cam and 01 trans. This is going to pose a problem trying to run it on an 03 pcm. 2003 transmissions are an odd one. They can't directly swap into anything but an 03. Same goes with trying to put a different year trans into your car. This is likely why your pcm needed to be an 01. I believe the best route for you would be to remove the few codes and smile.
