My grandfather (grandson of Thomas Randall Stap) says the family were of dutch origins and came from a ship building family in Grimsby. There was a Thomas Stap born in Grimsby in 1741. he is the only Stap I can find from there.
His occupation is listed as Sailor, so he could have migrated from Grimsby, Lincolnshire to Deal (in kent) where he married mary Wortham , and then joined the coastguard and settled in Dover.