Yikes. Sorry about your unfortunate deaths. It definitely sounds like mink or martin or weasel to me as well. Although they are noted for eating heads as well. If there are more than one dead at one time and no evidence of holes dug, wires broken in the coop. All a weasel needs anywhere is 2 inches of space and it is game on for the weasel family. They will if given the chance kill all the birds and eat one. I have had this happen on several occasions and have suffered big losses just in one night.
If you see and holes in the ground around the cage at all and about the size of a tennis ball or even smaller them buggers can burrow anywhere. If you are handy a stream, river,lake,etc. it is possible these critters. They are hard to catch. I use 2 methods personally. I use a live trap with a chicken corpse inside or I will add a small cage on the end of the live trap with a live chicken in it. The weasel,mink or whatever cannot gain access to the bird to harm it but once inside the live trap you got em. My other method is a little cruel but it works as well. I have a free range flock but I built a wooden box or an upsidedown apple crate and drill in two small openings, enough that the animal can get in and no chickens can gain access to inside the box. I put a dish of car antifreeze inside and the sweet smell and taste intices the weasel where it will drink it. It will poison the weasel eventually. I also have 2 barn cats (roger and Mouser), big boys as well. They are my protectors for the birds. They hate mink and rats. They keep me vermin free now and I can rest easier...
Hope some of us can be helpful. It really sucks when you lose your pets like that and can't control the outcome. Best of luck. Steve(BunkyB)
OH before I go, check for little dark brown or black poops around the coop. About 1/2 inch long like oversized rice. That will be rats. They hate each other so if a mink is around then there will be NO rats around. Mink poops are bigger and are kinda torpedo shaped.