Seems pretty obvious that it is not intended for use with a recessed receptacle, but rather to minimize the amount it sticks out from a flush receptacle. The latter would be more useful to most folks. If you are doing custom installation, it is time to customize. And who knows, perhaps the manufacturer offers the kind of line cord you need as an option.
FWIW I would not try "carving up" the existing plug. I would replace it with an more appropriate one for the situation.