Oh good! I've lived in the USA even longer than did Hermione, and I've been cringing, because until last week the same applied to me concerning the AE meaning!I seem to be more familiar than most with British English, but I've never seen/heard "graft" used to mean "hard work". (Or if I did, I mistakenly took it for the American meaning.)
In a quick family survey, my husband, too, first cited the BE meaning. But my adult children both cited the AE meaning and neither knew the BE one. I conclude that it is not a word my spouse or I use often.