Ah yes, As God said to Moses " I AM the I AM" tell them "I AM" has sent thee. "I AM" is definitely who the Lord God is. And as you stated Jesus said: "Before Abraham was, I AM." So this statement is evidence indeed that Jesus claimed to be God, which Aslan rejects.
The apostle John also states in John 1:2 that Jesus was in the beginning with God. And John 1:10 says Jesus created all things. So the apostle John who was an eyewitness to Jesus statements knew that Jesus claimed to be God. Why can't the heretic Aslan accept this?
In regards to "Their religious law", it was "their religious law" that they accused Jesus of breaking. Because the Old Testament permitted acts of Mercy on the Sabbath, Yet the Jewish leaders accused Jesus of breaking the Sabbath because he healed a man. But Jesus never broke God's Sabbath law as defined in the Old Testament as you have stated correctly, he broke "their law," the man made regulations and expectations that the religious leaders had tacked onto God's law. That's all that I was trying to say. People still do that today in regards to a strict interpretation of what is required on the Sabbath.