Those damage boosts DOES EFFECTdo effect melee override skills,skills; you simply tested with a poor skill choice. That OVERRIDESoverrides the melee attack with a NON-melee attack.
I am certain the Mechromancer claws are effected by weapon bladesblades; in my times I have used only melee and hide of terra against enemies. Roid rage damage certainly effects it too. I have seen the same results with the Gunzerker uppercut, effected by all the melee boosts that effect normal melee attacks.
Otherwise, the melee override for Zer0 would basically be the worst-spent skill point ever, right? It would negate any melee bonuses he had as long as he was attacking from deception.