Tell the neighbors to feed their cats a little better. If you're saying the neighbor has 10 to 15 cats then the answer is simple. Just contact animal control services. There's a limit to how many pets you can have. I have cats, both young and old at the moment, and several bird feeders. Of the hundreds of bird visits per day the cats are lucky to even come close to getting a bird with the exception of a lucky once in a blue moon attempt. Hell, most of the time the older two cats just watch the birds while sitting in the shade or behind a snowbank and seldom put forth the energy. Probably because their food bowl is always full. The youngest cat will always take a shot at getting a bird. Even if he just ate but that phase grows old real quick.
Now, if the neighbors cat steps paw in the yard....different story. I don't hesitate popping a stray cat and I assume the reverse is true if my pet wanders 40 acres over to the closest neighbors place. Fortunately I don't have to cover it up at all. If I had to I wouldn't leave any evidence laying around to alert the entire neighborhood and worse yet have some little kid see their dead pet laying on the road. I'd get rid of the critter somewhere else. Pets, especially cats, disappear and never come back all the time. Cause unknown.
If all else fails the parents of a recent girlfriend went through the same type of scenario and they live right in town. They put their bird feeders higher up off the ground and some chicken wire, maybe it was rabbit fencing, around the base of the feeder. It was shaped slightly like a funnel so no cats could climb up the wire and jump in. Birds eat in safety due to the height of the feeders and when the birds feel they have to hit the ground for the spilled seed they are protected by the wire. I use to call it the birdcage. They also planted Clematis, a flowering perrenial vine, that covers the wire each year. It's very little work or expense and it solved the problem completely and it looks pretty slick during the summer. One of the last times I was there was early fall and I watched several birds eating from the ground while the ex's own cat kept circling. If he couldn't find a solution after months of trying I doubt any other cat did either.
What you do in the dark will someday come to light.