You didn't mention the 40 foot gorge/precipice that takes off from your tomato garden 20 feet from the back door. If it wasn't for the smell, I'd say dump them in the flowline of the creek way down there. As beautiful as it is to look into the mid-height of those cottonwoods and sycamores that grow up so huge, if they bring bad things into your life that Cincy doesn't understand, the answer has to be an ongoing subtle extermination project that buries the dead on your property in such a way that benefits. I think you are doing exactly the right thing. Add some oak and poplar chips from someone's limb clearance to make a great mulch stew.
I use red oak, basket oak, poplar and tupelo chips (no pine!), from downed trees to hardwood leaves, kitchen waste, dead vermin, and the used up dirt from the garden to make fantastic graden soil in only two years. It cooks so hot in the winter that snow won't stick to it. If I turn it over in the cold weather it steams like its on fire. Dead ground hogs are the key. They are 80% fat, and they break down into great material for digestion of the organic stuff from the yard and woods. You'd have to put the pile at the end of the driveway slab, I guess, to keep neighbors from sticking a nose in.