All of your modal sentences have changed the original meaning.
You can't change a sentence that states what is to one that states what should be or should have been, or must be etc. without a change in meaning.
"He was speaking English in a French class" does not mean the same as "He should not have been speaking English in a French class." All of your modal sentences are inferences, or subjective judgements about the purely factual original sentences.
If adding a modal auxiliary left sentences unchanged in meaning, we wouldn't have much use for them.
Student or Learner