In a similar way that the best chess engine developer is not the best chess player there's little reason to think that the best person to detect chess engine use is the best player.
>includes having the entire tree of variations for every position in your mind while investigating
Too bad even Magnus can't do that and the closest you can get is by writing software to do it for you.
You did not describe the algorithm or the data which would help writing the software you are talking about. As I said, for me if this software would be based on comparing the engine's best move with the human's move and give such metrics as average centipawn loss, it would not be nearly adequate for this purpose.
And I insist that all the things you described as the hardest part are only poor substitutes for understanding the game of chess.