cantor,
A good definition of a Godol is someone who other Rabbonim, cross-denominational (within Orthodoxy), seek guidance and responsa from. i.e. Rav Eliyashiv, The Skulener Rebbe, and the Babi Sali (to pick 3 names) all did all of this for Jews of Sefardic, Chasidic, and Litvish (to pick 3 denominations) persuasion (meaning all of the 3 Rabbinical examples were sought by all of the 3 denominational examples). The names you mentioned did not. i.e. Rav Schachter is a big talmid chochom, but his halachic decisions is not generally sought as binding guidance outside of YU/MO circles. (Some of the other names you mentioned, were even more pronounced in this regard.)
And Rav Svei is sought after cross-denominationaly (as much as YU may not like this). So he would certainly fall into this category.