Ok, here is what I am thinking. It is overheating when you are stopped but not when moving. Therefore, when it is moving, enough cooling air is making it through the radiator to keep the motor cool. It really sounds like your electric fan isn't pulling enough air. I know I was really surprised just how big an electric had to be to do the proper cooling job. I would find out what your fan cfm is and do some research on what you might need.
As for the cover, I would be inclined to remove it so long as you have a fan shroud. Watch the temp real close to see what it is doing when you do.
Where are you located? I have heard of blocking off part of the radiator in colder climates during the winter. Is that a possibility, I know you got the radiator from someone else?
Good luck with it. I know the frustrations of trying to keep something cool.
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