This is a most interesting discussion.
Visitor1, far be it for me to judge the merits of anyone as Godol Hador. However the very term implies someone who is known and to whom the world’s Rabonim, Poskim and Roshei Yeshiva turn to for advice. There are many many ‘Shas Yiedden’ in the world who keep to themselves and for some reason are not known. Tzadik Hador, maybe, but Godol Hador implies more a leader, than a great, learned but hidden tzadik.
To me, and this is maybe an answer to yichusdik, I think Godol Hador may be interchangeable with the term that used to be used, Rabban shel kol b’nei Hagolah. This was used relatively recently, as a title for the Chofetz Chaim and R’ Chaim Ozer, and in my lifetime, R’ Moshe Feinstein.
ZD, I don’t know how it is in the American Torah World, but in EY and in Europe, Rav Steinman is known as Reb Aharon Leib.