Seems like a question from the "what if department".  Just my opinion, but so much work involved, and you would achieve very little.  Better to simply take a board and cut 2 lams from it.  Now fit them back together and add your Perry reflex, and build a bow.  Much less work involved.  You wont have a Self bow in either scenario, but you will have a chance to see what that kind of reflex adds, and some of the complexities involved.