Two points here really:
1 there is no incontrovertible proof that he claimed a unique sonship
I don’t know what he means by incontrovertible, but John 14:1-4 ”1’Do not let your hearts be troubled. Trust in God; trust also in me. 2In my Father's house are many rooms; if it were not so, I would have told you. I am going there to prepare a place for you. 3And if I go and prepare a place for you, I will come back and take you to be with me that you also may be where I am. 4You know the way to the place where I am going.’” seems to answer nicely.
2 unique sonship not open to other persons
Besides being redundant – any unique relationship is, by definition, not open to other persons – this misses the Point. While Jesus is the only begotten Son of God, we are all sons and daughters of God.