Do you live near a water source? River, pond, etc. One thing that most folks forget about is Mink. They will hunt during the day and often only drink the blood, hence the neck wounds on your birds. Although they get pretty large, and may not be able to fit through the size of opening you are describing, it could be a younger one. I had a few raccoon attacks this year - took five birds, three of which there were no trace but the tracks and the one we caught in the live trap. The other two were completely eaten... The tracks are throwing me off though as Weasels and Mink often walk on the balls of there feet and don't leave toe marks. Get a marsh mellow trap or two... if they are raccoon you will surely catch them that way.