My gg grandfather, David, was born in Old Buckenham, Norfolk around 1815. He had 2 younger brothers named Joseph and William. Joseph did emigrate to Canada a few years after my gg grandfather. William, as far as I can tell, stayed in England. The father of these boys was aJoseph Quantrill, who was born in 1776 in Old Buckenham. Joseph, was from a fairly large family, so that may be your missing link.
As far as the spelling of the last name, I have seen Quantrill, Quantrell, Quantrille and Quantrelle all from the Norfolk area. I have also seen documents where the spelling of the last name changed within the same family over 3 generations.
When I was in England about 12+ years ago, I was able to access a library in Norwich, Norfolk and found documentation from the 1500's that listed 2 brothers, a Richard and Robert Quantrill, living in the Norfolk area. This may be the starting point of the Quantrills in England - if one accepts the Hugoenot theory.
I joined the British website "Genes Reunited" about 3+ yeara ago and found it quite helpful in confirming my connection to the Norfolk, England area. I believe they still offer a free trial period, so you may want to explore that avenue, to see if there is information that may be more pertinent to you.
If I can be of any further assistance, please send me an email.