” the more leverage he can gain from his new fulcrum,”
While that has a nice sound to it, unfortunately one has no leverage at all from the fulcrum but on the longest arm.
Of course one can gain more leverage from a new fulcrum if that brings along with it a longer lever. There is nothing in my language that rules that out. And anyway, it is an image, a metaphor, a literary device ("a nice sound to it") which you acknowledge to have recognized, and, therefore, it is numbingly beside the point whether it is the fulcrum or the lever which produces the moment.