I knew when I took on having backyard barn animals that at some point I would have some sort of loss. That something would get one of my ladies or that they would get sick or something. But my last month of experience really threw me off of my rocker.
Several weeks ago I went and got new chickens. The Cream Legbar that I had was laying white eggs instead of the blue that she was supposed to be laying and the breeder was nice enough to get me another pullet that would for sure lay blue eggs. While there, 2 more pullets followed me home. There was a cross between a Cochin and a Road Island Red and a Maran/Cream Legbar cross. The Cochin I named Sweety Pie because that is exactly what she was and the Maran mix I named Heidi because she just seemed like a Heidi to me. 3 days in to having them the Cochin was killed by something and it ate her head and left the rest. Two weeks later the Cream Legbar (which I named Stinky because she smelled so bad on the way home) had gotten caught on a neighbors fence and been there for some time and when I got her down she died shortly after. It was really sad. I hated that she had gone through that. The temp was over 100 that day and she hung upside down, for God knows how long, before we found her. I feel so horrible about that. I just thought she was in the shade somewhere in my backyard. Then only a few days after that Heidi starts looking a little lethargic but still spunky when I got close to her one day and only hours later I walk out and find her dead with her legs int he air. Having never lost a chicken before I was shocked. All 3 different ways. My other girls are fine. No problems there for over 18 months. Have you ever had a sting of bad luck like that?
Sadly, due to not wanting to invite carnivores to come hang out in our backyard, I had to put their bodies in the landfill. That brought on guilt too. If you have chickens how do you deal with your carcasses when there is a loss?
I don't have chickens and thus don't have any advice to give you. just hugs and support from here. You have to remind yourself that nature is brutal. There were nothing you could do at the time to make any difference at all.. I would feel just as devastated, but remember it's not your fault.
We also put ours in the landfill. We had some horrid deaths. A magpie took the head off one of our quail who was a really lovely friendly bird. It's very grim. And we did feel bad.
In my experience carnivores will probably not come just to hang out at the prospect of a composted bird. But it does depend a bit on how you compost and where you can put them. If you do have a large compost (at least a cubic yard) moving material to get the dead birds into the middle can work very well. Putting the birds on top of a wire compost bin works too, if you can bury them in a good quantity of leaves, straw or wood chips. If you can smell them after a few days, you need more carbon rich material and you may feel better putting a “cover” or lid on the bin. We have had to do something like this on more than one occasion due to predators, and only rarely due to illness. If all else fails a burial is an option too. Even a fairly shallow hole can be protected with a flagstone or paver on top (to keep opportunists out) until a few months have passed and most of nature's work is done.
A bit of advice for introducing birds, it sounds like these 3 had learned a bit of a different life where you got them. A lot of chicken behavior is instinct (and birdbrain) but there are still some things they learn and that can impact their behavior. Birds that live under aerial net stop watching overhead for predators which puts them at risk that your other birds would notice and flee. My chickens will try to hop on and over anything that isn't an electric fence which means they would probably also have gone exploring and could have ended up in that exact stuck predicament. When I'm bringing in new birds I'll keep them a bit more confined until they get a bit more used to the place and maybe learn a few tricks from the locals. They are birdbrains though, really and truly. The number of birds I've lost because they really were just that stupid continues to astound me.
Better luck will follow, and everything is a learning experience. Don't let it get you down.