I had a friend note that in my writings about 'What defiles a person' a few days ago my statement that Jesus ignored was over the top. And so, he's correct. It may be more accurate to say re-interpret. Jesus did interpret and re-interpret the law in a different fashion than many of the Pharisees and scribes. I was writing more polemically - to wake the reader up - rather than academically, but the point is a good one. And in many ways Jesus was very close to the Pharisees, certainly closer to them than the other religio-political parties.
The question Jesus asks is more along the lines of "What is the purpose of the law?" and the Pharisees seem to be interested more in "What is the letter of the law?" Both are useful questions, but taken alone both questions lack a certain something that leads to a fullness of understanding. I, myself, have made quips and more determined examinations about the letter of the law as in when Leviticus says "You shall not lie with a man as awith a woman." saying I have no interest in lying with a man as with a woman, I want to lie with a man as with a man.
Yet the understanding of the law rests on more than quick summations and sarcastic retorts. There's a deeper understanding that comes from looking at the letter and the purpose that we should be seeking whenever we intepret what the law is.
I've seen some so interested in the purpose of the law that they forget to apply the law when something is clearly wrong and others so interested in the letter of the law that they forget the purpose of the law when the letter clearly harms both victim and victimized.
A news report the other day was about a woman who was raped. On the way to the station they found out she had a couple of warrents out. She had taken part one of a drug that prevents pregnancy/implantation, but in jail one of the attendants did not let her take the second part of the drug regimen to prevent pregnancy. The victim in this case was victimized by someone who thought they were upholding the law.
Paul, for all his emphasis on the law, does have an understanding - only after a knock on the side of the head on the way to Damascus - of what the law can and cannot do that we sometimes miss. My friend was correct to point that out. The law was given for our health and our support, but taken as the end of everything is death producing as you point out with your citation of 2 Cor 2:6
 Now when the Pharisees and some of the scribes who had come from
Jerusalem gathered around him,  they noticed that some of his
disciples were eating with defiled hands, that is, without washing them.