Has Trump's team argued that Trump is innocent in either case?

They cant argue the various acts did not happen. The documents show otherwise. So all they have is the unreliability of the witnesses, and the unfairness of the prosecution. Either of these contradict the documents. Of course, he will appeal..😷

Not even his supporters argue that. They typically either say:

1) What he did should not be a crime,
2) the crime was justified
3) others do the same thing but he is being singled out for political reasons.

Trump's immunity is not a jury issue at this point, just an issue for the appellate courts, so they can't pitch it quite like that to a jury.

Having said that, Judge Cannon might let them argue at least something pretty close to that if that case does go to trial.