I thought that the “non-Spanish Sephardim” intermarried with the original Spanish Sephardim over the past 500 years since the Spanish Sephardim moved into the countries of the Edah Hamizrach, to the extent that it is rare today that any Sephardi is anything other than of mixed heritage of original Spanish and original Edah Hamizrach.
Even the different minhagim of the original Edah Hamizrach and of the original Spanish Sephardim were usually combined into one nusach/minhagim. And more often than not the original Spanish nusach survived more than the original Edah Hamizrach nusach. That, for example, happened in Syria. This was because numerically the Spanish Sephardim were a lot more numerous in the places they moved to after the Inquisition than the numbers of Jews who lived there from before the Expulsion.