Im gonna hafta Dissagree.Fileing grooves across the back of the bow,will violate the growth ring on the back,and give it a place to separate.It may not happen now,but sooner or later,it will,if used much.
Snag,
the bows you saw,cut across the back,most likely had overlays on em.If it were me,id rasp the ends down,at an angle,toward the belly and take the groove away.then glue overlays on top.Or as you mentioned,you could pike the tips down and start over.