I can feel your pain; I see more coyotes in my neighborhood than in the woods - the frustration and embarrassment over the years.
But last Monday we jumped a large, dark chocolate male, it was too big, too close, and I only had a short barrel AR. Further my back is not up to moving any animal that large, so the future is not really an option for me.
However if you want I can give you directions to where he is. He leaves a large wake in the grass between the prairie and the swamp, so finding him should not be too difficult and due to location he is not likely to wonder too far in the next couple months. Just promise me some meat please.