You wrote: "How do we reconcile the traditional Exothermic & Endothermic graphs of Energy vs reaction process with the fact that the products must be more bound and have greater potential energy? Typically the endo / exo graphs show (for an exothermic reaction) that the reactants have more energy than the products."
The misconception here is in the notion that "more bound" is the same as "have greater potential energy".
In an exothermic reaction, the reactants reduce their combined potential energy which is transferred to the reacting system and its surroundings, often as kinetic energy; so the temperature of the system and its surrounds goes up, but the potential energy of the products has to be less than that of the reactants. The reverse is true for endothermic reactions, of course. So it's relatively easy to extract potential energy from the bonds in the reactants when burning methane in oxygen, but good luck trying to extract potential energy from the bonds in water and carbon dioxide (products). So in actuality "more bound" means "have less potential energy". Or, if you prefer, bond stability is greater when the bonds have less potential energy.
An exothermic reaction is analogous to a rock on a cliff edge falling to a lower level, increasing its stability by reducing its potential energy and heating up the surroundings. An endothermic reaction involves the rock spontaneously rising to increase its potential energy. Rocks on cliffs don't do this, but molecules regularly do. Besides reducing potential energy, the other driving force behind chemical reactions is entropy.
In terms of binding energy, in an exothermic reaction the products have greater binding energy than the reactants - the bonding in the products is stronger = incorporate less potential energy (than the bonding in the reactants) so more energy has to be inserted into those (product) bonds to disrupt them.
Regards,
George Przywolnik
Perth, Western Australia