Is it necessary to replace the engine control module after replacing coils?

You are bound and determined to replace the ECM aren't you, just go ahead and replace it and maybe waste your money. We can't help you if you have your mind set, and you don't have to repost every time. There are procedures for testing these problems, but go ahead and do it your way.

Have you checked the harness for wire damage? Change the PCM , then find the cause of the problem.