Yes, Christopher went down through the family - not my branch, as that had Johns and Williams.
To get back from William and Ann Green, you need to look at the Lincolnshire Marriage Bonds and you should find a couple of Christophers in there. The links from generation to generation are not conclusively proven, but once you realise that you are dealing with a very restricted surname group, the chances of there being more than one possible becomes almost minimal.
Basically, all roads seem to lead back to Great Carlton.