In his work of she'eloth u-teshuvoth - Shu"T Ohr Yisshaq, Yoreh De'ah, Siman 24 "She'eloth Qessaroth - HaRav Yisshaq `Abadi shlit"a records the following (translation mine):
You asked: Concerning a Sepharadi who wants to eat at a wedding or in a restaurant which has a non-Jewish chef and the kosher supervisor is Ashkenazi (and according to their halakhic methodology it is enough that a Jew lights the fire used for cooking, but for Sepharadim it is not), is he able to eat there?
Answer: It is possible for a Sepharadi to also rely on this [halakhic methodology of the Ashekenazim], since we have two arguments for leniency in this regard:  The opinion of the Rem"a that the making of the fire is enough, and  the halakhic methodologies of other Rishonim which do not attribute to the cooking of hired workers and day-laborers the status of bishul aku"m - even if they are not specifically the employees of a Jew. Only when one is staying at the house of a non-Jew and the food is cooked in the house of a non-Jew is it then forbidden [according to these Rishonim].
Thus, it seems that there is weight on the Sephardic side of the question that would allow Sepharadim to eat in such kosher restaurants. As regards hekhsherim which rely on similar leniencies as with the restaurants in question, I know that Rav `Abadi also holds such products to be kosher for Sepharadim as well, although I have not found a formal teshuvah in his sefer Shu"T Ohr Yisshaq to that effect.