Where Jesus comments on heavy rules imposed by men, we can assume it's Shammai and where Jesus comments on God's standards being lowered by men, we can assume it's Hillel.
???
I don't see how you can assume anything of the sort.
In order to substantiate the idea that any "stated standard" had been violated you would have to produce such a standard from the Law. The reality is Jesus had instituted a newer and stricter standard than had existed under the Law where a man was allowed to divorce a wife for reasons other than infidelity.
Jesus' primary bone of contention with Pharisees throughout the Gospels was with rigid interpretation. While it's certainly true that Jesus advocated a much more positive view of women than had existed among the Jews of the period, that is his principal disagreement with the school of Hillel. Time after time after time in the Gospels, he advocates their liberal interpretation of the Law.
He is so close to Hillel that a number of Jewish scholars argue that Jesus himself was a Pharisee. And this is one of the reasons that the controversy stores are so perplexing to Jews today. Jesus appears to be jousting at windmills because the position he takes vis a vis the Law is that of normative Judaism.