The combination of Churchward and Parrott suggests that your family originated from Devon, England. The area around Berry Pomeroy and Stoke Gabriel seems most likely but your grandparents may not have been the immigrant generation, ie you may not find their names on any of the passenger lists. However, it might be worth looking for that particular combination of surnames to see if members of a local community travelled together.

Have you tried
http://www.churchward.com/cw/ or the P_rr_tt Society?