Jesus always hammered on the Pharisees not for their hard sayings but for being hypocrites, in other words talking the talk but not walking the walk, like not supporting their parents while they demanded that others followed that part of the law. 

Later in the Gospel of Matthew last verse of chapter 5 Jesus tells us "to be perfect as the father is perfect" This encapsulates what his expectations are for his disciples. Jesus lost many followers because they thought his sayings were too harsh, not the other way around. 

What does the spirit of the law mean concretely, you are coming with an interpretation that seems to have no anchor in the words of Christ, other than to water his words and hard saying to platitudes. 

Surely the spirit of the law is to embrace it as a love offering to God, by loving his laws and his will, and living in his truth. Not rejecting them for personal comfort and being a hypocrite like the Pharisees, who picked and chose what they wanted to follow.