There are not many known synonyms for the word "Ashburtonite." Some possible alternatives could be "resident of Ashburton," "Ashburton local," or "Ashburton denizen." However, these terms do not carry the same level of specificity and distinctiveness as the original word. Ashburtonite refers specifically to someone who resides in or is connected to Ashburton, a town in the east of Devon, England. Therefore, it may be best to stick with this term in order to accurately convey this particular meaning. Additionally, using an adjective form such as "Ashburtonian" could also be a suitable alternative.