Life is full of co-incidences, but there must be something in all these name repititions.
The American branch also shows how the FROSTICK name is interchangeable with FROSTWICK which first appears in older records in Norfolk, UK. There is still a thriving Frostick/Frostwick community in Norfolk, especially in the area northwest of Norwich and towards the coast. Towns like Aylesham, Wroxham and Wood Dalling are in this area where the shop signs and local graveyards are full of Frosticks.
I feel certain that there lies the origin of the family, and this was originally a Viking stronghold and a center at the times when England was divided into Danelaw and Saxon areas by an East/West divide.