If several of my surnames appear on the list of Jewish surnames, do I have a better chance?

No. It is necessary to prove consanguinity with a Sephardic Jew. This is required by law. The mere fact of having a surname does not imply that the person in question is a descendant of a Sephardic Jew. The reasons for which a person may have a surname are very diverse and it is not always consanguinity. Apart from this, it is also necessary to consider that there are many surnames that were common to the three creeds that coexisted in Spain: Muslim, Jewish and Christian. Even more so in the case of patronymic surnames such as Núñez, Méndez, García and many others, which do not imply in any case that the person is of Jewish origin.