The only source I have seen for a birth year of about 1360 for R' Akiva the Elder is this from the About sections of both R' Akiva the Elde and his son R' Yizach:
Sources: Title (book): "A world apart: a memoir of Jewish life in nineteenth century Galicia", Author: Joseph Margoshes, Ira Robinson, Rebecca Margolis. p. 184
I have now reviewed the Margoshes book and did find the reference to R' Akiva, but there is no birth year given. Here is the complete quote from p. 184:
"8) His Excellency, our teacher Rabbi Hayyim Katz, brother of His Excellency Rabbi Akiva Katz of Oben, leader and executive in the city of Prague, may his memory be a blessing, son of his Excellency, our teacher Isaac Katz, head of the rabbinic court in the districts of Galata and Pera in the capital city of Constantinople, son of his Excellency Akiva Kohen Zedek, pure Sephardi, head of the rabbinical court of Salonika, may his memory be a blessing, who was among the exiles of Spain and was accepted as head of the rabbinical court of Salonika."
It is misleading to put these dates and then cite the Margoshes book as the source.
This wording is reminiscent of one of the Hebrew books previously cited in discussions and it is likely that the author of the above genealogy, Rabbi Eliezer Lippa Gartenhoyz, got the information from that same Hebrew book.
The important point is that nowhere is the year 1360 mentioned or even suggested in the Margoshes book, and therefore there is no actual source for that birth year, as far as I know. I am therefore estimating a later birth year of about 1425. Based on the various biographies presented in these discussions it seems that R' Akiva the Elder and his son R' Yitzach went into exile at different times, the former directly from Spain and the latter via the Portugal route, and that all three generations, R' Akiva the Elder, R' Yitzach, and R' Akiva of Uban must have been born in Spain. I have not seen any direct statement about when R' Akiva of Uban departed from Iberia.
The question of Menahem being the father of R' Akiva of Uban will have to await for someone who can read the sources given in the Encyclopedia Judaica for this information.
I do not believe there are any other stones remaining unturned, and in the absence of any evidence to the contrary I myself am going accept a Sephardic origin for R' Akiva the Elder. To each their own conclusions.....