They actually kindly replied almost right away to my inquire: apparently at the beginning of the Brooklyn team era they used several BB types (including the one that I have in my frame) and only later they resorted with the one with the Gt logo cutout. Unfortunately they said that that BB is a generic one and it cannot be attributed at a specific framebuilder.
The Gios attribution of the eBay frame mostly depends on the characteristic seat stay and mine is entirely different...