You keep mentioning Judaism as if they correctly observed God's law - they didn't as Jesus points out in Mat.23 (and many other scripts). So why would Jesus then want to stick to Judaism ???Why would he create another religion?
As far as i know he thought of the Judaism as containing the law of God, and he didn't think of himself as higher than God. So he would stick to it. He had no reason to create a new religion.
Certainly he would still use the Tanakh. Giving new interpretations to the writtings.
Jesus gives us the correct ways to keep God's law and because it had not been taught and practiced it is seen as NEW, or new interpretation as you call it. But it would NOT BE JUDAISM with the exception of the sabbath day which belongs to God anyway.
As seen from Luk.6v46 neither do christians keep God's law correctly and when Christ returns he will introduce God's law correctly and be seen as ' a new and living way'. God's law will then be kept and practiced.