Instead of fighting city hall it might be a good idea to designate a spot, not on the grass, but perhaps on some rocks or soil where you need to train him to go. Still need to dilute with water because the odor will kill you. I have an Aussie and Standard Poodle that love the back downspout and have killed the grass there. When we landscape in the back I plan on putting a rock bed of some sort at that spot for them to use. Have a hose right there as well so will be managable.
Thanks for saying he is using your yard 'cause boy would things get rolling otherwise!!!