Indeed Miguel, it was very common for the spaniards to take local wives, not only in the Philippines but within all of the Spanish Empire, being this the reason why the majority of mexicans have both indian and spanish blood. Also, there have been migrations of spaniards to places like Mexico, not only during colonial times but as early as the XX century, not only basque, but from all over Spain.
Regarding the Casa de Contratación, it was the authority mainly responsible for controlling inmigration to the Spanish colonies, but probably not the only one. Perhaps a better way to look for ancestors is in Church records (specially baptisisms, which include family ancestors): you look at your fathers´records, then your grandfather, and at some point you will end up in Spain. This is one of the most efficient ways to look up for ancestors in Mexico, since before the separation of Church and State, the Catholic Church was the authority responsible for people´s records. The Philippines should not be any exception.