Muchos Gracias!
The information you gave is very interesting. Your research looks like the immigration from to the Americas came for military reasons to populate the new territories.
My suspicions are this. Spain has not really come to terms with what it did in the 1500's. Spanish text books are still not likely to call the Spanish Inquisition what it was - a crime against humanity. Many people were taken from their Jewish and Muslim parents and force into situations where joining the military and moving to the ends of the earth would seem better then staying in "civilized Europe."
My suspicion still stands that the Arroyos were in fact Jews until the Spanish Inquisition.
My father (Antonio Arroyo Jr) was from Mexico and orphaned early in his life. My mother's people settled in New Mexico. They are not Arroyo's but they were also running away from the Spanish Inquisition.
Although we are not Jewish now, we do have a strong Judaic influence in our customs and food.
I would suggest reading between the lines of the text books in Spain. And asking local Jewish leaders (if you can find any) for the truth about the Inquisition.