I found this thread when researching an explanation for why a man called Joseph Maskrey living in the parish of Kedliston (Derbyshire) married a woman called Esther Pearson at St George's, Hanover Square by licence in 1769. They then had three sons christened at Edlaston, Derbyshire. It seems a long way to go to be married and while I know it was fashionable to be married at St George's the woman (Esther Pearson) could not sign her name and the man (Joseph Maskrey) though he did sign, was probably a cotton dealer, and so not very high up the social scale at the time. If Esther was genuinely resident in the parish, and had met Joseph even though he lived in Derbyshire, then why did they not marry by banns?
My research interest is not the same as yours but the following may be relevant to your discussion.
In addition to the marriages witnessed by Caleb Greville at St George's there are apparently christenings in the neighbouring parish of St James witnessed by both a William Greville and a Caleb Greville (http://corry-history.blogspot.com/2007/07/our-corry-relatives.html). There is a record (as already noted) of Caleb Greville describing himself as "the clerk at St George's Hanover- square" when giving evidence to the Old Bailey in a bigamy case in June 1793. These facts suggest there is a Caleb Greville who is a church official.
There is an IGI record of a christening of Caleb Grivell, son of William Grivell in St Anne Soho in October 1738, and an IGI record of a marriage between Caleb Grevill and Esther Paterson in All Hallows Staining in October 1757. There are also IGI birth records of various children of Caleb and Esther such as Esther in January 1766.