I can report that further in-depth work on this family in 2016 has now categorically excluded the link back to Surrey. The head of the tree is Robert SHIERS (c1630-1682), a tanner from the town of Bicester in Oxfordshire. The synopsis has been updated accordingly.
Robert's origins are not known, however it is confirmed his children settled in Chilvers Coton near Nuneaton (Warwickshire), from which many modern SHIERS families are descended.
Regards,
Mark